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Maps completely preserving spectral functions |
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| Authors: | Li Huang Jinchuan Hou |
| Institution: | a Department of Mathematics, Taiyuan University of Science and Technology, Taiyuan 030024, PR China b Department of Mathematics, Taiyuan University of Technology, Taiyuan 030024, PR China c Department of Mathematics, Shanxi University, Taiyuan 030006, PR China |
| Abstract: | Let X,Y be infinite dimensional complex Banach spaces and A,B be standard operator algebras on X and Y, respectively. In this paper, we show that surjective maps completely preserving certain spectral function Δ(·) from A to B are isomorphisms, where Δ(·) stands for any one of 13 spectral functions σ(·), σl(·), σr(·), σl(·)∩σr(·), ∂σ(·), ησ(·), σp(·), σc(·), σp(·)∩σc(·), σp(·)∪σc(·), σap(·), σs(·), and σap(·)∩σs(·). |
| Keywords: | Primary: 47B49 47A12 |
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