算子代数上的可乘映射(英文)

Multiplicative Maps on Operator Algebras

本文得到算子代数 B( X)上可乘映射的一个结构定理 .在此基础上 ,刻画了算子代数上保秩、保余秩、保谱、保谱半径、保恒等和的可乘映射 ,进而 ,通过可乘映射刻画了B( X)

In this paper, a structure theorem of abstract multiplicative maps on B(X) is given, where X is a Banach space with dimX=∞. Based on this structure theorem, the multiplicative maps on B(X) are characterized if they are rank-preserving, corank-preserving, spectrum-preserving, spectral radius-preserving, or identity-sum-preserving. Moreover, new characterizations of isomorphisms and conjugate isomorphisms on B(X) are given in terms of multiplicative maps.