On operators which attain their norm on every reducing subspace

Ramesh, G. and Osaka, H. (2022) On operators which attain their norm on every reducing subspace. Annals of Functional Analysis, 13 (2). ISSN 2639-7390

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Abstract

In this article, first, we study the spectral properties of operators which attain their norm on every reducing subspace and then we study the structure of normal and quasinormal operators in this class. At the end we give a description of paranormal operators whose adjoint is also paranormal. This gives a direct proof of the fact that an operator is normal if and only if the operator and its adjoint are paranormal. © 2022, Tusi Mathematical Research Group (TMRG).

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IITH Creators:

IITH Creators	ORCiD
Ramesh, G.	UNSPECIFIED

Item Type:

Article

Additional Information:

G. Ramesh’s research is supported by SERB Grant no. MTR/2019/001307, Govt. of India. H. Osaka’s research is supported by KAKENHI Grant no. JP20K03644. The authors are grateful to the referee for the comments and suggestions which are useful in improving the readability of the paper.

Uncontrolled Keywords:

Norm attaining operator; Orthogonal projection; Reducing subspace; Unitary operator

Subjects:

Mathematics

Divisions:

Department of Mathematics

Depositing User:

. LibTrainee 2021

Date Deposited:

22 Jul 2022 09:15

Last Modified:

22 Jul 2022 09:15