Characterizations of Centralizable Mappings on Algebras of Locally Measurable Operators |
| |
| Authors: | Jun HE Guang Yu AN Jian Kui LI Wen Hua QIAN |
| |
| Institution: | 1. Department of Mathematics, Anhui Polytechnic University, Wuhu 241000, P. R. China;
2. Department of Mathematics, Shaanxi University of Science and Technology, Xi'an 710021, P. R. China;
3. Department of Mathematics, East China University of Science and Technology, Shanghai 200237, P. R. China;
4. School of Mathematical Sciences, Chongqing Normal University, Chongqing 401331, P. R. China |
| |
| Abstract: | A linear mapping φ from an algebra A into its bimodule M is called a centralizable mapping at G ∈ A if φ(AB)=φ(A)B=Aφ(B) for each A and B in A with AB=G. In this paper, we prove that if M is a von Neumann algebra without direct summands of type I1 and type II, A is a *-subalgebra with M ⊆ A ⊆ LS(M) and G is a fixed element in A, then every continuous (with respect to the local measure topology t(M)) centralizable mapping at G from A into M is a centralizer. |
| |
| Keywords: | Centralizable mapping centralizer von Neumann algebra locally measurable operator |
|
| 点击此处可从《数学学报(英文版)》浏览原始摘要信息 |
| 点击此处可从《数学学报(英文版)》下载免费的PDF全文 |
|
