On weakly unitarily invariant norm and the λ-Aluthge transformation for invertible operator |
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| Authors: | Kazuyoshi Okubo |
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| Institution: | Mathematics Laboratory, Hokkaido University of Education, Sapporo College, 5-3-1-5 Ainosato, Kitaku, Sapporo 002-8502, Japan |
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| Abstract: | Let T∈B(H) be an invertible operator with polar decomposition T = UP and B∈B(H) commute with T. In this paper we prove that ∣∣∣PλBUP1−λ∣∣∣ ? ∣∣∣BT∣∣∣, where ∣∣∣ · ∣∣∣ is a weakly unitarily invariant norm on B(H) and 0 ? λ ? 1. As the consequence of this result, we have ∣∣∣f(PλUP1−λ)∣∣∣ ? ∣∣∣f(T)∣∣∣ for any polynomial f. |
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| Keywords: | 15A60 47A12 47A63 |
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