In this paper, a real-time computation method for the control problems in differential-algebraic systems is presented. The errors of the method are estimated, and the relation between the sampling stepsize and the con...In this paper, a real-time computation method for the control problems in differential-algebraic systems is presented. The errors of the method are estimated, and the relation between the sampling stepsize and the controlled errors is analyzed. The stability analysis is done for a model problem, and the stability region is ploted which gives the range of the sampling stepsizes with which the stability of control process is guaranteed.展开更多
Let A. （R） be a real Clifford algebra and Gan open connected set in R<sup>n</sup> . By [1], the function with val-ues in A<sub>n</sub> （R） may be written aswhere B ={r<sub>1</sub&g...Let A. （R） be a real Clifford algebra and Gan open connected set in R<sup>n</sup> . By [1], the function with val-ues in A<sub>n</sub> （R） may be written aswhere B ={r<sub>1</sub>,r<sub>2</sub>,…,r<sub>h</sub>} {1,2,…,n}represent that from the sum for’lst and 2nd indi-sates respectively, and we have the following result.Theorem A Function f （x） with values in A. （R） is regular in G if and only ifLet G be the unit hyperball and L the unit hypersphere. Cutting G by the plane: x<sub>3</sub>= a<sub>3</sub>, …,x<sub>n</sub> = a<sub>n</sub>（n3） , we obtain a section domain G<sub>a</sub> in the x<sub>1</sub>x<sub>2</sub> plane. Let L<sub>a</sub> be the boundary of G<sub>a</sub>, and its center is writ-ten as 0<sub> </sub> = （0,0,α<sub>3</sub>,...,α<sub>n</sub>） .展开更多
Let A and B be C^＊-algebras. An extension of B by A is a short exact sequence O→A→E→B→O. （＊） Suppose that A is an AT-algebra with real rank zero and B is any AT-algebra. We prove that E is an AT-algebra if an...Let A and B be C^＊-algebras. An extension of B by A is a short exact sequence O→A→E→B→O. （＊） Suppose that A is an AT-algebra with real rank zero and B is any AT-algebra. We prove that E is an AT-algebra if and only if the extension （＊） is quasidiagonal.展开更多
We characterise the positive cone of a real C^(*)-algebra geometrically.Given an open coneΩin a real Banach space V,with the closureΩ,we show thatΩis the interior of the positive cone of a unital real C^(*)-algebra...We characterise the positive cone of a real C^(*)-algebra geometrically.Given an open coneΩin a real Banach space V,with the closureΩ,we show thatΩis the interior of the positive cone of a unital real C^(*)-algebra if and only if it is a Finsler symmetric cone with an orientable extension,which is equivalent to the condition that V is,in an equivalent norm,the Hermitian part of a unital real C^(*)-algebra with the positive coneΩ.展开更多
In this paper,we study real Banach * algebras systematically.We present the right form of Pták’s inequality[1,4]in the real case,and generalize the results of Vukman in[3]to the general case(algebras with or wit...In this paper,we study real Banach * algebras systematically.We present the right form of Pták’s inequality[1,4]in the real case,and generalize the results of Vukman in[3]to the general case(algebras with or without an identity).Moreover,this paper is a real analogue of Pták’s work[1] in the complex case.展开更多
Let ■ be a real semisimple Lie algebra, ■ be a Cartan subalgebra of ■, Aut (■) be the automorphism group of ■ and Ad( ■ ) be the inner automorphism group of (?). Definition 1. The group ((?))={σ|(?); σ∈Aut((?...Let ■ be a real semisimple Lie algebra, ■ be a Cartan subalgebra of ■, Aut (■) be the automorphism group of ■ and Ad( ■ ) be the inner automorphism group of (?). Definition 1. The group ((?))={σ|(?); σ∈Aut((?))and σ(η) =η}is called the Cartan group of (?) with respect to (?).展开更多
In this paper,we show that a topologically irreducible * representation of a real C~*- algebra is also algebraically irreducible.Moreover,the properties of pure real states on a real C~*- algebra and their left kernel...In this paper,we show that a topologically irreducible * representation of a real C~*- algebra is also algebraically irreducible.Moreover,the properties of pure real states on a real C~*- algebra and their left kernels are discussed.展开更多
We prove analogs of the Kaplansky Density Theorem and the Kadison Transitivity Theorem for irreducible representations of a real C＊-algebra on a real Hilbert space. Specifically, if a C＊-algebra is acting irreducibl...We prove analogs of the Kaplansky Density Theorem and the Kadison Transitivity Theorem for irreducible representations of a real C＊-algebra on a real Hilbert space. Specifically, if a C＊-algebra is acting irreducibly on a real Hilbert space, then the Hilbert space has either a real, complex, or quaternionic structure with respect to which the density and transitivity theorems hold.展开更多
In this paper, we point out that most results on abelian (complex) W~*-algebras hold in the real case. Of course, there are differences in homeomorphisms of period 2. Moreover, an abelian real Von Neumann algebra not ...In this paper, we point out that most results on abelian (complex) W~*-algebras hold in the real case. Of course, there are differences in homeomorphisms of period 2. Moreover, an abelian real Von Neumann algebra not containing any minimal projection on a separable real Hilbert space is * isomorphic to L_r~∞([0,1]) (all real functions in L~∞ ([0, 1])), or L~∞([0, 1])(as a real W~*-algebra), or L_r~∞([0,1]) L_∞([0, 1]) (as a real W~*-algebra), and it is different from the complex case.展开更多
Let A be a unital simple C-algebra of real rank zero,stable rank one,with weakly unperforated K<sub>0</sub>（A）and unique normalized quasi-trace τ,and let X be a compact metric space.We show that two mon...Let A be a unital simple C-algebra of real rank zero,stable rank one,with weakly unperforated K<sub>0</sub>（A）and unique normalized quasi-trace τ,and let X be a compact metric space.We show that two monomorphisms Φ,Ψ:C（X）→A are approximately unitarily equivalent if and only if Φ and Ψ induce the same element in KL（C（X）,A）and the two linear functionals τ ο Φ and τ ο Φ are equal.We also show that,with an injectivity condition,an almost multiplicative morphism from C（X） into A with vanishing KK-obstacle is close to a homomorphism.展开更多
文摘In this paper, a real-time computation method for the control problems in differential-algebraic systems is presented. The errors of the method are estimated, and the relation between the sampling stepsize and the controlled errors is analyzed. The stability analysis is done for a model problem, and the stability region is ploted which gives the range of the sampling stepsizes with which the stability of control process is guaranteed.
文摘Let A. （R） be a real Clifford algebra and Gan open connected set in R<sup>n</sup> . By [1], the function with val-ues in A<sub>n</sub> （R） may be written aswhere B ={r<sub>1</sub>,r<sub>2</sub>,…,r<sub>h</sub>} {1,2,…,n}represent that from the sum for’lst and 2nd indi-sates respectively, and we have the following result.Theorem A Function f （x） with values in A. （R） is regular in G if and only ifLet G be the unit hyperball and L the unit hypersphere. Cutting G by the plane: x<sub>3</sub>= a<sub>3</sub>, …,x<sub>n</sub> = a<sub>n</sub>（n3） , we obtain a section domain G<sub>a</sub> in the x<sub>1</sub>x<sub>2</sub> plane. Let L<sub>a</sub> be the boundary of G<sub>a</sub>, and its center is writ-ten as 0<sub> </sub> = （0,0,α<sub>3</sub>,...,α<sub>n</sub>） .
文摘Let A and B be C^＊-algebras. An extension of B by A is a short exact sequence O→A→E→B→O. （＊） Suppose that A is an AT-algebra with real rank zero and B is any AT-algebra. We prove that E is an AT-algebra if and only if the extension （＊） is quasidiagonal.
基金supported by the Engineering and Physical Sciences Research Council,UK(Grant No.EP/R044228/1).
文摘We characterise the positive cone of a real C^(*)-algebra geometrically.Given an open coneΩin a real Banach space V,with the closureΩ,we show thatΩis the interior of the positive cone of a unital real C^(*)-algebra if and only if it is a Finsler symmetric cone with an orientable extension,which is equivalent to the condition that V is,in an equivalent norm,the Hermitian part of a unital real C^(*)-algebra with the positive coneΩ.
基金This work is supported in part by research grants of NSF of China (the first author)of the Chinese University of Hong Kong (both authors).
文摘In this paper,we study real Banach * algebras systematically.We present the right form of Pták’s inequality[1,4]in the real case,and generalize the results of Vukman in[3]to the general case(algebras with or without an identity).Moreover,this paper is a real analogue of Pták’s work[1] in the complex case.
基金Project supported by the National Natural Science Foundation of China.
文摘Let ■ be a real semisimple Lie algebra, ■ be a Cartan subalgebra of ■, Aut (■) be the automorphism group of ■ and Ad( ■ ) be the inner automorphism group of (?). Definition 1. The group ((?))={σ|(?); σ∈Aut((?))and σ(η) =η}is called the Cartan group of (?) with respect to (?).
基金Partially supported by the National Natural Science Foundation of China.
文摘In this paper,we show that a topologically irreducible * representation of a real C~*- algebra is also algebraically irreducible.Moreover,the properties of pure real states on a real C~*- algebra and their left kernels are discussed.
文摘We prove analogs of the Kaplansky Density Theorem and the Kadison Transitivity Theorem for irreducible representations of a real C＊-algebra on a real Hilbert space. Specifically, if a C＊-algebra is acting irreducibly on a real Hilbert space, then the Hilbert space has either a real, complex, or quaternionic structure with respect to which the density and transitivity theorems hold.
文摘In this paper, we point out that most results on abelian (complex) W~*-algebras hold in the real case. Of course, there are differences in homeomorphisms of period 2. Moreover, an abelian real Von Neumann algebra not containing any minimal projection on a separable real Hilbert space is * isomorphic to L_r~∞([0,1]) (all real functions in L~∞ ([0, 1])), or L~∞([0, 1])(as a real W~*-algebra), or L_r~∞([0,1]) L_∞([0, 1]) (as a real W~*-algebra), and it is different from the complex case.
基金Research partially supported by NSF Grants DMS 93-01082(H.L)and DMS-9401515(G.G)This work was reported by the first named author at West Coast Operator Algebras Seminar(Sept.1995,Eugene,Oregon)
文摘Let A be a unital simple C-algebra of real rank zero,stable rank one,with weakly unperforated K<sub>0</sub>（A）and unique normalized quasi-trace τ,and let X be a compact metric space.We show that two monomorphisms Φ,Ψ:C（X）→A are approximately unitarily equivalent if and only if Φ and Ψ induce the same element in KL（C（X）,A）and the two linear functionals τ ο Φ and τ ο Φ are equal.We also show that,with an injectivity condition,an almost multiplicative morphism from C（X） into A with vanishing KK-obstacle is close to a homomorphism.
