Certain free products are introduced for operator spaces and dual operator spaces.It is shown that the free product of operator spaces does not preserve the injectivity. The linking C*-algebra of the full free product...Certain free products are introduced for operator spaces and dual operator spaces.It is shown that the free product of operator spaces does not preserve the injectivity. The linking C*-algebra of the full free product of two ternary rings of operators (simply, TRO's) is *-isomorphic to the full free product of the linking C*-algebras of the two TRO's. The operator space-reduced free product of the preduals of von Neumann algebras agrees with the predual of the reduced free product of the von Neumann algebras. Each of two operator spaces can be embedded completely isometrically into the reduced free product of the operator spaces. Finally, an example is presented to show that the C*-algebra-reduced free product of two C*-algebras may be contractively isomorphic to a proper subspace of their reduced free product as operator spaces.展开更多
1 Introduction and main resultsARVESON in ref. [1] generalized the classical Hahn-Banach Extension Theorem for linear func-tionals to the self-adjoint linear closed subspace of C~* -algebras. From then on numerous au-...1 Introduction and main resultsARVESON in ref. [1] generalized the classical Hahn-Banach Extension Theorem for linear func-tionals to the self-adjoint linear closed subspace of C~* -algebras. From then on numerous au-thors have given various generalizations of the non-commutative Hahn-Banach-Arveson Theo-rem of ref. [1]. The following extension theorem is due to G. Wittstock.展开更多
文摘Certain free products are introduced for operator spaces and dual operator spaces.It is shown that the free product of operator spaces does not preserve the injectivity. The linking C*-algebra of the full free product of two ternary rings of operators (simply, TRO's) is *-isomorphic to the full free product of the linking C*-algebras of the two TRO's. The operator space-reduced free product of the preduals of von Neumann algebras agrees with the predual of the reduced free product of the von Neumann algebras. Each of two operator spaces can be embedded completely isometrically into the reduced free product of the operator spaces. Finally, an example is presented to show that the C*-algebra-reduced free product of two C*-algebras may be contractively isomorphic to a proper subspace of their reduced free product as operator spaces.
基金This work was supported by the National Natural Science Foundation of China (Grant No. 19671042).
文摘1 Introduction and main resultsARVESON in ref. [1] generalized the classical Hahn-Banach Extension Theorem for linear func-tionals to the self-adjoint linear closed subspace of C~* -algebras. From then on numerous au-thors have given various generalizations of the non-commutative Hahn-Banach-Arveson Theo-rem of ref. [1]. The following extension theorem is due to G. Wittstock.
基金Supported by the Zhejiang Qianjiang Talent Program in 2008the Program for New Century Excellent Talents in University of Ministry of Education of China in 2010+1 种基金the National Natural Science Foundation of China(Grant No.11271321)the Fundamental Research Funds of Zhejiang University
文摘In this note, we show that avon Neumann algebra M is injective if and only if the weak＊ similarity degree d.（M） ≤ 2.
