Let M be a full Hilbert C＊-module over a C＊-algebra A, and let End^（.A4） be the algebra of adjointable operators on M. We show that if A is unital and commutative, then every derivation of End＊A（M） is an inner ...Let M be a full Hilbert C＊-module over a C＊-algebra A, and let End^（.A4） be the algebra of adjointable operators on M. We show that if A is unital and commutative, then every derivation of End＊A（M） is an inner derivation, and that if A is a-unital and commutative, then innerness of derivations on ＂compact＂ operators completely decides innerness of derivations on EndA（M）. If .4 is unital （no commutativity is assumed） such that every derivation of A is inner, then it is proved that every derivation of EndA（Ln（A）） is also inner, where Ln（A） denotes the direct sum of n copies of A. In addition, in case A is unital, commutative and there exist xo,yo ∈M such that 〈xo,yo〉 = 1, we characterize the linear A-module homomorphisms on EndA（M） which behave like derivations when acting on zero products.展开更多
We present here a realization of Hurwitz algebra in terms of 2 × 2 vector matrices which maintain the correspondence between the geometry of vector spaces that is used in the classical physics and the algebraic f...We present here a realization of Hurwitz algebra in terms of 2 × 2 vector matrices which maintain the correspondence between the geometry of vector spaces that is used in the classical physics and the algebraic foundation underlying quantum theory. The multiplication rule we use is a modification of the one originally introduced by M. Zorn. We demonstrate that our multiplication is not intrinsically non-associative;the realization of the real and complex numbers is commutative and associative, the real quaternions maintain associativity and the real octonion matrices form an alternative algebra. Extension to the calculus of the matrices (with Hurwitz algebra valued matrix elements) of the arbitrary dimensions is straightforward. We briefly discuss applications of the obtained results to extensions of standard Hilbert space formulation in quantum physics and to alternative wave mechanical formulation of the classical field theory.展开更多
Extending the notion of property T of finite von Neumann algebras to general yon Neu- mann algebras, we define and study in this paper property T＊＊ for （possibly non-unital） C＊-algebras. We obtain several results...Extending the notion of property T of finite von Neumann algebras to general yon Neu- mann algebras, we define and study in this paper property T＊＊ for （possibly non-unital） C＊-algebras. We obtain several results of property T＊＊ parallel to those of property T for unital C＊-algebras. Moreover, we show that a discrete group F has property T if and only if the group C＊-algebra C＊（F） （or equivalently, the reduced group C＊-algebra C＊（F）） has property T＊＊. We also show that the compact operators K（g2） has property T＊＊ but co does not have property T＊＊.展开更多
This paper discusses quantum mechanical schemas for describing waves with non-abelian phases, Fock spaces of annihilation-creation operators for these structures, and the Feynman recipe for obtaining descriptions of p...This paper discusses quantum mechanical schemas for describing waves with non-abelian phases, Fock spaces of annihilation-creation operators for these structures, and the Feynman recipe for obtaining descriptions of particle interactions with external fields.展开更多
In this paper we define and study chain conditions for Hilbert C＊-modules through their C＊-algebras of compact operators and discuss their perseverance under Morita equivalence and tensor products. We show that thes...In this paper we define and study chain conditions for Hilbert C＊-modules through their C＊-algebras of compact operators and discuss their perseverance under Morita equivalence and tensor products. We show that these chain conditions are passed from the C＊-algebra to its Hilbert module under certain conditions. We also study chain conditions for Hilbert modules coming from inclusion of C＊-algebra with a faithful conditional expectation.展开更多
本文讨论了C代数中的全正映射,推广了[1]中命题2.5的结果。本文利用[2]中的记号、设H_i是Hilbert空间,H_1(?)H_2是H_1与H_2的代数张量积,任给ξ=sum from I=1 to n ξ_(1I)(?)ξ_(2I)∈H_1(?)H_2,η=sum from j=1 to m η_(1j)(?)η_(2j...本文讨论了C代数中的全正映射,推广了[1]中命题2.5的结果。本文利用[2]中的记号、设H_i是Hilbert空间,H_1(?)H_2是H_1与H_2的代数张量积,任给ξ=sum from I=1 to n ξ_(1I)(?)ξ_(2I)∈H_1(?)H_2,η=sum from j=1 to m η_(1j)(?)η_(2j)∈H_1(?)H_2,定义(ξ,η)=sum from n=I,j (ξ_(1i),η_(1j))(ξ_(2j),η_(2j)),由[2],(,)是H_1(?)H_2中的内积。H_1(?)H_2的完备化,用H_1(?)H_2表示,其是a是由H_1(?)H_2中内积导出的范数(见[1]p182)。展开更多
基金supported by National Natural Science Foundation of China(Grant No.11171151)Natural Science Foundation of Jiangsu Province of China(Grant No.BK2011720)supported by Singapore Ministry of Education Academic Research Fund Tier1(Grant No.R-146-000-136-112)
文摘Let M be a full Hilbert C＊-module over a C＊-algebra A, and let End^（.A4） be the algebra of adjointable operators on M. We show that if A is unital and commutative, then every derivation of End＊A（M） is an inner derivation, and that if A is a-unital and commutative, then innerness of derivations on ＂compact＂ operators completely decides innerness of derivations on EndA（M）. If .4 is unital （no commutativity is assumed） such that every derivation of A is inner, then it is proved that every derivation of EndA（Ln（A）） is also inner, where Ln（A） denotes the direct sum of n copies of A. In addition, in case A is unital, commutative and there exist xo,yo ∈M such that 〈xo,yo〉 = 1, we characterize the linear A-module homomorphisms on EndA（M） which behave like derivations when acting on zero products.
文摘We present here a realization of Hurwitz algebra in terms of 2 × 2 vector matrices which maintain the correspondence between the geometry of vector spaces that is used in the classical physics and the algebraic foundation underlying quantum theory. The multiplication rule we use is a modification of the one originally introduced by M. Zorn. We demonstrate that our multiplication is not intrinsically non-associative;the realization of the real and complex numbers is commutative and associative, the real quaternions maintain associativity and the real octonion matrices form an alternative algebra. Extension to the calculus of the matrices (with Hurwitz algebra valued matrix elements) of the arbitrary dimensions is straightforward. We briefly discuss applications of the obtained results to extensions of standard Hilbert space formulation in quantum physics and to alternative wave mechanical formulation of the classical field theory.
文摘Extending the notion of property T of finite von Neumann algebras to general yon Neu- mann algebras, we define and study in this paper property T＊＊ for （possibly non-unital） C＊-algebras. We obtain several results of property T＊＊ parallel to those of property T for unital C＊-algebras. Moreover, we show that a discrete group F has property T if and only if the group C＊-algebra C＊（F） （or equivalently, the reduced group C＊-algebra C＊（F）） has property T＊＊. We also show that the compact operators K（g2） has property T＊＊ but co does not have property T＊＊.
文摘This paper discusses quantum mechanical schemas for describing waves with non-abelian phases, Fock spaces of annihilation-creation operators for these structures, and the Feynman recipe for obtaining descriptions of particle interactions with external fields.
文摘In this paper we define and study chain conditions for Hilbert C＊-modules through their C＊-algebras of compact operators and discuss their perseverance under Morita equivalence and tensor products. We show that these chain conditions are passed from the C＊-algebra to its Hilbert module under certain conditions. We also study chain conditions for Hilbert modules coming from inclusion of C＊-algebra with a faithful conditional expectation.
文摘本文讨论了C代数中的全正映射,推广了[1]中命题2.5的结果。本文利用[2]中的记号、设H_i是Hilbert空间,H_1(?)H_2是H_1与H_2的代数张量积,任给ξ=sum from I=1 to n ξ_(1I)(?)ξ_(2I)∈H_1(?)H_2,η=sum from j=1 to m η_(1j)(?)η_(2j)∈H_1(?)H_2,定义(ξ,η)=sum from n=I,j (ξ_(1i),η_(1j))(ξ_(2j),η_(2j)),由[2],(,)是H_1(?)H_2中的内积。H_1(?)H_2的完备化,用H_1(?)H_2表示,其是a是由H_1(?)H_2中内积导出的范数(见[1]p182)。
