C^*代数上pseudo DMP逆的研究

在条件a=abb^(1,3)、bc=ca,b^*c=ca*及ab=ba下研究pseudo DMP逆及dual pseudo DMP逆在C^*代数上特征及反序。同时,根据m-EP元素的定义与性质,探讨C^*代数上pseudo DMP逆、dual pseudo DMP逆和Moore-Penrose逆的关系。

Complete Positivity of Elementary Operators on C^＊—algebras

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.

Injective Envelopes of a Hilbert C~*Module

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 .

An Introduction to the Theory of C~*-modules

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.

Some Inequalities about the Positive Elements in C~*-Algebra

In this paper, we discussed some improtant inequalities, such as young inequality, Holder inequality and Minkowski inequality,about the positive elements in C~*-Algebra.

Diagonal Invariant Ideals of Topologically Graded C~*-algebras

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.

The smash products of entwining structure

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.

Completely Positive Definite Maps Over Topological-algebras

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.

Characteristic Functions over C*-Probability Spaces

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.

Asymptotic Direct System of C^(*)-algebras and Locally AF-algebra

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.

HYERS—ULAM—RASSIAS STABILITY OF QUADRATIC FUNCTIONAL EQUATIONS IN BANACH MODULES OVER A C^＊—ALGEBRA

The authors prove the Hyers-Ulam-Rassias stability of the quadratic mapping in Banachmodules over a unital C*-algebra, and prove the Hyers-Ulam-Rassias stability of the quadraticmapping in Banach modules over a unital Banach algebra.

THE INDUCED REPRESENTATION OF C^＊-GROUPOID DYNAMIC SYSTEMS

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.

Lie Ideals in AF C~*-Algebras

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.

TOEPLITZ OPERATORS AND ALGEBRAS ON DIRICHLET SPACES

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.

THE FUNDAMENTAL GROUP OF THE AUTOMORPHISM GROUP OF A NONCOMMUTATIVE TORUS THE FUNDAMENTAL GROUP OF THE AUTOMORPHISM GROUP OF A NONCOMMUTATIVE TORUS

Assume that each completely irrational noncommutative torus is realized as an inductive limit of circle algebras, and that for a completely irrational noncommutative torus Aω of rank m there are a completely irrational noncommutative torus Aρ of rank m and a positive integer d such that tr（Aω） = tr（Aρ）. It is proved that the set of all C*-algebras of sections of locally trivial C*-algebra bundles over S2 with fibres Aω. has a group structure, denoted by π1（Aut（Aω.））, which is isomorphic to Z if d > 1 and {0} if d > 1. Let Bcd be a cd-homogeneous C*-algebra over S2 x T2 of which no non-trivial matrix algebra can be factored out. The spherical noncommutative torns Sρcd is defined by twisting C*（T2 x Zm-2） in Bcd C* （Z（m-2）） by a totally skew multiplier ρ on T2 x Z（m-2）. It is shown that Sρcd Mp∞ is isomorphic to C（S2） C* （T2 x Zm-2, ρ） Mcd（C） Mp∞ if and only if the set of prime factors of cd is a subset of the set of prime factors of p.

Superderivation Algebras of Modular Lie Superalgebras of ■-Type

The authors consider a family of finite-dimensional Lie superalgebras of C-type over an algebraically closed field of characteristic p 〉 3. It is proved that the Lie superalgebras of C-type are simple and the spanning sets are determined. Then the spanning sets are employed to characterize the superderivation algebras of these Lie superalgebras. Finally, the associative forms are discussed and a comparison is made between these Lie superalgebras and other simple Lie superalgebras of Cartan type.

GENERALIZED SIMPLE NONCOMMUTATIVE TORI

The generalized noncommutative torus Tkp of rank n was defined in [4] by the crossed product Am/k ×a3 Z ×a4 … ×an Z, where the actions ai of Z on the fibre Mk(C) of a rational rotation algebra Am/k are trivial, and C*(kZ × kZ) ×a3 Z ×a4 ... ×an Z is a completely irrational noncommutative torus Ap of rank n. It is shown in this paper that Tkp is strongly Morita equivalent to Ap, and that Tkp (?) Mp∞ is isomorphic to Ap (?) Mk(C) (?) Mp∞ if and only if the set of prime factors of k is a subset of the set of prime factors of p.

Wiener-Hopf Operators on Discrete Abelian Groups

The groupoid approach to study Wiener-Hopf operators on discrete abelian groups is realized.

IRRATIONAL ROTATION c-ALGEBRA FOR GROUPOID c-ALGEBRA

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.

THE TRACE SPACE INVARIANT AND UNITARY GROUP OF C-ALGEBRA

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.