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 εL(H), 0<r<1,T has nontrivial (hyper-)invariant subspace ifT(r, 1−r) does.
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This research was supported by the National Natural Science Foundation of China.
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Chen, L., Zikun, Y. & Yingbin, R. Common properties of operatorsRS andSR andp-hyponormal operators. Integr equ oper theory 43, 313–325 (2002). https://doi.org/10.1007/BF01255566
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DOI: https://doi.org/10.1007/BF01255566