First, that prime C~* -algebras with countable primitive ideals are all primitive C*-algebras is proved. Then the proof that prime C~* -algebras with property RR(A) = 0 are all primitive C~*-algebras is given.
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First, that prime C~* -algebras with countable primitive ideals are all primitive C*-algebras is proved. Then the proof that prime C~* -algebras with property RR(A) = 0 are all primitive C~*-algebras is given.
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.
