Additive maps on standard operator algebras preserving parts of the spectrum |
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| Authors: | Jianlian Cui Jinchuan Hou |
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| Institution: | a School of Mathematical Sciences, Peking University, Beijing 100871, PR China
b Department of Mathematics, Shanxi Teachers University, Linfen 041004, PR China |
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| Abstract: | Let  and  be standard operator algebras on infinite dimensional complex Banach spaces X and Y, respectively, and let Φ be a unital additive surjection from  onto  . We introduce thirteen parts of the spectrum for elements in  and  , and prove that if Φ preserves any one of these parts of the spectrum, then it is either an isomorphism or an anti-isomorphism. |
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| Keywords: | Additive preservers Parts of spectrum Standard operator algebras |
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