Totally P-posinormal operators are subscalar |
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Authors: | R. Nickolov Zh. Zhelev |
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Affiliation: | (1) Faculty of Mathematics and Informatics, Shoumen University, 9712 Shoumen, Bulgaria |
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Abstract: | LetH be a complex infinite-dimensional separable Hilbert space. An operatorT inL(H) is called totally P-posinormal (see [9]) iff there is a polynomialP with zero constant term such that for each, whereTz=T–zI andM(z) is bounded on the compacts of C. In this paper we prove that every totally P-posinormal operator is subscalar, i.e. it is the restriction of a generalized scalar operator to an invariant subspace. Further, a list of some important corollaries about Bishop's property and the existence of invariant subspaces is presented. |
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Keywords: | 47B20 47A11 47A15 |
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