2-LOCAL ISOMETRIES OF SOME OPERATOR ALGEBRAS

Proceedings of the Edinburgh Mathematical Society

Lajos Molnár¹ 

关键词: operator algebra;    isometry;    local isometry;   

DOI  :  10.1017/S0013091500000043

学科分类：数学（综合）

来源: Cambridge University Press

【 摘 要 】

As a consequence of the main result of the paper we obtain that every 2-local isometry of the $C^*$-algebra $B(H)$ of all bounded linear operators on a separable infinite-dimensional Hilbert space $H$ is an isometry. We have a similar statement concerning the isometries of any extension of the algebra of all compact operators by a separable commutative $C^*$-algebra. Therefore, on those $C^*$-algebras the isometries are completely determined by their local actions on the two-point subsets of the underlying algebras.AMS 2000 Mathematics subject classification: Primary 47B49

【 授权许可】

Unknown