This paper,combined algebraical structure with analytical system,has studied the part of theory of C~*-modules over A by using the homolgical methods, where A is a commutative C~*-algebra over complex number field C. ...This paper,combined algebraical structure with analytical system,has studied the part of theory of C~*-modules over A by using the homolgical methods, where A is a commutative C~*-algebra over complex number field C. That is to say we have not only defined some relevant new concept,but also obtained some results about them.展开更多
In this paper, we discussed some improtant inequalities, such as young inequality, Holder inequality and Minkowski inequality,about the positive elements in C~*-Algebra.
We study diagonal invariant ideals of topologically graded C*-algebras over discrete groups. Since all Toeplitz algebras defined on discrete groups are topologically graded, the results in this paper have improved the...We study diagonal invariant ideals of topologically graded C*-algebras over discrete groups. Since all Toeplitz algebras defined on discrete groups are topologically graded, the results in this paper have improved the first author's previous works on this topic.展开更多
In this paper, we discuss completely positive definite maps over topological algebras. A Schwarz type inequality for n-positive definite maps, and the Stinespring representation theorem for completely positive definit...In this paper, we discuss completely positive definite maps over topological algebras. A Schwarz type inequality for n-positive definite maps, and the Stinespring representation theorem for completely positive definite maps over topological algebras are given.展开更多
Various properties of the characteristic functions of random variables in a non-commutative C*-probability space are studied in this paper. It turns out that the distributions of random variables are uniquely determin...Various properties of the characteristic functions of random variables in a non-commutative C*-probability space are studied in this paper. It turns out that the distributions of random variables are uniquely determined by their characteristic functions. By using the properties of characteristic functions, a central limit theorem for a sequence of independent identically distributed random variables in a C*-probability space is established as well.展开更多
As in homology, the notion of injectivity is introduced in the category whose objects are Hilbert C * module over a C * algebra and whose morphism are bounded module operators. The definition of injective envelope...As in homology, the notion of injectivity is introduced in the category whose objects are Hilbert C * module over a C * algebra and whose morphism are bounded module operators. The definition of injective envelopes of an extension of a Hilbert C * modules over a C * algebra is introduced, and is characterized in terms of the injectivity and essence. It is shown that every Hilbert C * module has a unique (up to H isometrics) injective envelope if it exists. It is also shown that an extension of a Hilbert C * module is an injective envelope if and only if it is an injective and essential extension. Moreover, every Hilbert C * module over a W * algebra has a unique (up to H isometrics) injective envelope and the injective envelope of a Hilbert C * module H is maximal essential extension of H .展开更多
Let k be a commutative ring, C a projective k-coalgebra. The smash productsof entwining structure (A, C)_ψ are discussed. When the map ψ is a bijective, and C is a finitelygenerated k-module, a version of the Ulbric...Let k be a commutative ring, C a projective k-coalgebra. The smash productsof entwining structure (A, C)_ψ are discussed. When the map ψ is a bijective, and C is a finitelygenerated k-module, a version of the Ulbrich theorem for coalgebras C is given.展开更多
Let E(x) = be an elementary operator on a C-algebra A. We prove that if A is prime with soc(A) = 0, or there is a family of irreducible representation of A such that is faithful and (A) does not contain compact operat...Let E(x) = be an elementary operator on a C-algebra A. We prove that if A is prime with soc(A) = 0, or there is a family of irreducible representation of A such that is faithful and (A) does not contain compact operator,or A has a faithful repre sentation π such that π(A)″with no central portions of type In for n>1 then E is positive if and only if E is completely positive.展开更多
We define the direct limit of the asymptotic direct system of C^(*)-algebras and give some properties of it.Finally,we prove that a C^(*)-algebra is a locally AF-algebra,if and only if it is the direct limit of an asy...We define the direct limit of the asymptotic direct system of C^(*)-algebras and give some properties of it.Finally,we prove that a C^(*)-algebra is a locally AF-algebra,if and only if it is the direct limit of an asymptotic direct system of finite-dimensional C^(*)-algebras.展开更多
We study Lie ideals in unital AF C^＊-algebras. It is shown that if a linear manifold L in an AF C^＊-algebra A is a closed Lie ideal in A, then there exists a closed associative ideal I and a closed subalgebra EI of ...We study Lie ideals in unital AF C^＊-algebras. It is shown that if a linear manifold L in an AF C^＊-algebra A is a closed Lie ideal in A, then there exists a closed associative ideal I and a closed subalgebra EI of the canonical masa D of A such that [A,I]^- belong to L belong to I ＋ EI, and that every closed subspace in this form is a closed Lie ideal in A.展开更多
This paper characterizes the irrational rotaion C-algebra associated with the Toeplitz Calgebraover the L-shaped domain in in the sense of the maximal radical series, which is an isomorphism invariant.
Let A be a unital C-algebra, n ∈ N ∪ {∞}. It is proved that the isomorphism △n : is isometric for some suitable distances. Asan application, the author has the split exact sequence with iA contractive (and isometr...Let A be a unital C-algebra, n ∈ N ∪ {∞}. It is proved that the isomorphism △n : is isometric for some suitable distances. Asan application, the author has the split exact sequence with iA contractive (and isometric if n = ∞) under certain condition of A.展开更多
Little is known about how chronic inflammation contributes to the progression of hepatoceUular carcinoma （HCC）, especially the initiation of cancer. To uncover the critical transition from chronic inflammation to HC...Little is known about how chronic inflammation contributes to the progression of hepatoceUular carcinoma （HCC）, especially the initiation of cancer. To uncover the critical transition from chronic inflammation to HCC and the molecular mechanisms at a network level, we analyzed the time-series proteomic data of woodchuck hepatitis virus/c.myc mice and age-matched wt-C57BL/6 mice using our dynamical network biomarker （DNB） model. DNB analysis indicated that the 5th month after birth of transgenic mice was the critical period of cancer initiation, just before the critical transition, which is consistent with clinical symptoms. Meanwhile, the DNB-associated network showed a drastic inversion of protein expression and coexpression levels before and after the critical transition. Two members of DNB, PLA2G6 and CYP2C44, along with their associated differentially expressed proteins, were found to induce dysfunction of arachidonic acid metabolism, further activate inflammatory responses through inflammatory mediator regulation of transient receptor potential channels, and finally lead to impairments of liver detoxification and malignant transition to cancer. As a c-Myc target, PLA2G6 positively correlated with c-Myc in expression, showing a trend from decreasing to increasing during carcinogenesis, with the minimal point at the critical transition or tipping point. Such trend of homologous PLA2G6 and c-Myc was also observed during human hepatocarcinogenesis, with the minimal point at high-grade dysplastic nodules （a stage just before the carcinogenesis）. Our study implies that PLA2G6 might function as an oncogene like famous c-Myc during hepatocar- cinogenesis, while downregulation of PLA2G6 and c-Myc could be a warning signal indicating imminent carcinogenesis.展开更多
The author studies the relation of continuous-trace property between C*-algebra A and the fixed point C*-algebra Aα in certain C*-dynamic system (A, G, α) by introducing an α-invariant continuous trace property. F...The author studies the relation of continuous-trace property between C*-algebra A and the fixed point C*-algebra Aα in certain C*-dynamic system (A, G, α) by introducing an α-invariant continuous trace property. For separable C*-dynamic system (A, G, α) with G compact and abelian,A liminal, αt ∈ AutCb(A) (A) and pointwise unitary, the necessary and sufficient condition for A to be continuous-trace, which contains Aα continuousitrace, is obtained.展开更多
Let G be a second countable locally compact groupoid with Haar system {λu}, H be a closed subgroupoid containing Go with Haar system {λuH}. T.Masuda introduced the C*-Groupoid dynamic system (G, A, α) and its reduc...Let G be a second countable locally compact groupoid with Haar system {λu}, H be a closed subgroupoid containing Go with Haar system {λuH}. T.Masuda introduced the C*-Groupoid dynamic system (G, A, α) and its reduced crossed product Cr.d(G, A) in [2], where A is a C*-algebra, α is the homomorphism G→Aut(A). In this paper the author introduces the C*-groupoid dynamic systems (H, A, α|H) and (H\G2, A, α) induced by (G, A, α) and proves that C~*red(H, A) and C~*red(H\G2, A) are strongly Morita equivalent. Moreover the induced representation from C~*red(H, A) to C~*red(G, A) is got.展开更多
This paper is a continuation of [1]. It gives some applications of the results in [1], containing some examples of pure-infinite AF-algebras and the invariant properties of the types of the C-extensions by two AF-alge...This paper is a continuation of [1]. It gives some applications of the results in [1], containing some examples of pure-infinite AF-algebras and the invariant properties of the types of the C-extensions by two AF-algebras of the same type.展开更多
The automorphism group of the Toeplitz C^*- algebra, J(C^1), generated by Toeplitz op-erators with C^1-symbols on Dirichlet space D is discussed; the K0, K1-groups and the first cohomology group of J(C^1) are compute...The automorphism group of the Toeplitz C^*- algebra, J(C^1), generated by Toeplitz op-erators with C^1-symbols on Dirichlet space D is discussed; the K0, K1-groups and the first cohomology group of J(C^1) are computed. In addition, the author proves that the spectra of Toeplitz operators with C^1-symbols are always connected, and discusses the algebraic prop-erties of Toeplitz operators.In particular, it is proved that there is no nontrivial selfadjoint Toeplitz operator on D and Tψ^* = Tψ^- if and only if Tψ is a scalar operator.展开更多
文摘This paper,combined algebraical structure with analytical system,has studied the part of theory of C~*-modules over A by using the homolgical methods, where A is a commutative C~*-algebra over complex number field C. That is to say we have not only defined some relevant new concept,but also obtained some results about them.
文摘In this paper, we discussed some improtant inequalities, such as young inequality, Holder inequality and Minkowski inequality,about the positive elements in C~*-Algebra.
基金Supported by the National Natural Science Foundation of China(10371051)
文摘We study diagonal invariant ideals of topologically graded C*-algebras over discrete groups. Since all Toeplitz algebras defined on discrete groups are topologically graded, the results in this paper have improved the first author's previous works on this topic.
文摘In this paper, we discuss completely positive definite maps over topological algebras. A Schwarz type inequality for n-positive definite maps, and the Stinespring representation theorem for completely positive definite maps over topological algebras are given.
基金the Shanghai Science and Technology Commission, No. 01ZA14003.
文摘Various properties of the characteristic functions of random variables in a non-commutative C*-probability space are studied in this paper. It turns out that the distributions of random variables are uniquely determined by their characteristic functions. By using the properties of characteristic functions, a central limit theorem for a sequence of independent identically distributed random variables in a C*-probability space is established as well.
文摘As in homology, the notion of injectivity is introduced in the category whose objects are Hilbert C * module over a C * algebra and whose morphism are bounded module operators. The definition of injective envelopes of an extension of a Hilbert C * modules over a C * algebra is introduced, and is characterized in terms of the injectivity and essence. It is shown that every Hilbert C * module has a unique (up to H isometrics) injective envelope if it exists. It is also shown that an extension of a Hilbert C * module is an injective envelope if and only if it is an injective and essential extension. Moreover, every Hilbert C * module over a W * algebra has a unique (up to H isometrics) injective envelope and the injective envelope of a Hilbert C * module H is maximal essential extension of H .
文摘Let k be a commutative ring, C a projective k-coalgebra. The smash productsof entwining structure (A, C)_ψ are discussed. When the map ψ is a bijective, and C is a finitelygenerated k-module, a version of the Ulbrich theorem for coalgebras C is given.
文摘Let E(x) = be an elementary operator on a C-algebra A. We prove that if A is prime with soc(A) = 0, or there is a family of irreducible representation of A such that is faithful and (A) does not contain compact operator,or A has a faithful repre sentation π such that π(A)″with no central portions of type In for n>1 then E is positive if and only if E is completely positive.
基金Supported by Natural Science Foundation of Jiangsu Province,China (No.BK20171421)。
文摘We define the direct limit of the asymptotic direct system of C^(*)-algebras and give some properties of it.Finally,we prove that a C^(*)-algebra is a locally AF-algebra,if and only if it is the direct limit of an asymptotic direct system of finite-dimensional C^(*)-algebras.
基金the National Natural Science Foundation of China (10371016)
文摘We study Lie ideals in unital AF C^＊-algebras. It is shown that if a linear manifold L in an AF C^＊-algebra A is a closed Lie ideal in A, then there exists a closed associative ideal I and a closed subalgebra EI of the canonical masa D of A such that [A,I]^- belong to L belong to I ＋ EI, and that every closed subspace in this form is a closed Lie ideal in A.
文摘This paper characterizes the irrational rotaion C-algebra associated with the Toeplitz Calgebraover the L-shaped domain in in the sense of the maximal radical series, which is an isomorphism invariant.
基金Project supported by the National Natural Science Foundation of China (No.10271090).
文摘Let A be a unital C-algebra, n ∈ N ∪ {∞}. It is proved that the isomorphism △n : is isometric for some suitable distances. Asan application, the author has the split exact sequence with iA contractive (and isometric if n = ∞) under certain condition of A.
文摘Little is known about how chronic inflammation contributes to the progression of hepatoceUular carcinoma （HCC）, especially the initiation of cancer. To uncover the critical transition from chronic inflammation to HCC and the molecular mechanisms at a network level, we analyzed the time-series proteomic data of woodchuck hepatitis virus/c.myc mice and age-matched wt-C57BL/6 mice using our dynamical network biomarker （DNB） model. DNB analysis indicated that the 5th month after birth of transgenic mice was the critical period of cancer initiation, just before the critical transition, which is consistent with clinical symptoms. Meanwhile, the DNB-associated network showed a drastic inversion of protein expression and coexpression levels before and after the critical transition. Two members of DNB, PLA2G6 and CYP2C44, along with their associated differentially expressed proteins, were found to induce dysfunction of arachidonic acid metabolism, further activate inflammatory responses through inflammatory mediator regulation of transient receptor potential channels, and finally lead to impairments of liver detoxification and malignant transition to cancer. As a c-Myc target, PLA2G6 positively correlated with c-Myc in expression, showing a trend from decreasing to increasing during carcinogenesis, with the minimal point at the critical transition or tipping point. Such trend of homologous PLA2G6 and c-Myc was also observed during human hepatocarcinogenesis, with the minimal point at high-grade dysplastic nodules （a stage just before the carcinogenesis）. Our study implies that PLA2G6 might function as an oncogene like famous c-Myc during hepatocar- cinogenesis, while downregulation of PLA2G6 and c-Myc could be a warning signal indicating imminent carcinogenesis.
文摘The author studies the relation of continuous-trace property between C*-algebra A and the fixed point C*-algebra Aα in certain C*-dynamic system (A, G, α) by introducing an α-invariant continuous trace property. For separable C*-dynamic system (A, G, α) with G compact and abelian,A liminal, αt ∈ AutCb(A) (A) and pointwise unitary, the necessary and sufficient condition for A to be continuous-trace, which contains Aα continuousitrace, is obtained.
文摘Let G be a second countable locally compact groupoid with Haar system {λu}, H be a closed subgroupoid containing Go with Haar system {λuH}. T.Masuda introduced the C*-Groupoid dynamic system (G, A, α) and its reduced crossed product Cr.d(G, A) in [2], where A is a C*-algebra, α is the homomorphism G→Aut(A). In this paper the author introduces the C*-groupoid dynamic systems (H, A, α|H) and (H\G2, A, α) induced by (G, A, α) and proves that C~*red(H, A) and C~*red(H\G2, A) are strongly Morita equivalent. Moreover the induced representation from C~*red(H, A) to C~*red(G, A) is got.
文摘This paper is a continuation of [1]. It gives some applications of the results in [1], containing some examples of pure-infinite AF-algebras and the invariant properties of the types of the C-extensions by two AF-algebras of the same type.
文摘The automorphism group of the Toeplitz C^*- algebra, J(C^1), generated by Toeplitz op-erators with C^1-symbols on Dirichlet space D is discussed; the K0, K1-groups and the first cohomology group of J(C^1) are computed. In addition, the author proves that the spectra of Toeplitz operators with C^1-symbols are always connected, and discusses the algebraic prop-erties of Toeplitz operators.In particular, it is proved that there is no nontrivial selfadjoint Toeplitz operator on D and Tψ^* = Tψ^- if and only if Tψ is a scalar operator.
