Common properties of operatorsRS andSR andp-hyponormal operators |
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Authors: | Lin Chen Yan Zikun Ruan Yingbin |
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Institution: | (1) Department of Mathematics, Fujian Normal University, 350007 Fuzhou, The People's Republic of China |
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Abstract: | LetR andS be bounded linear operators on a Bananch space. We discuss the spectral and subdecomposable properties and properties concerning invariant subspaces common toRS andSR. We prove that, by these properties,p-hyponormal and log-hyponormal operators and their generalized Aluthge transformations are all subdecomposable operators;T andT(r, 1–r)(0<r<1) have same spectral structure and equal spectral parts ifT denotesp-hyponormal or dominant operator; for everyT L(H), 0<r<1,T has nontrivial (hyper-)invariant subspace ifT(r, 1–r) does.This research was supported by the National Natural Science Foundation of China. |
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Keywords: | Primary 47B99 47A10 |
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