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.
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Acknowledgements
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.
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Communicated by Jean-Christophe Bourin.
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Ramesh, G., Osaka, H. On operators which attain their norm on every reducing subspace. Ann. Funct. Anal. 13, 19 (2022). https://doi.org/10.1007/s43034-022-00167-8
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DOI: https://doi.org/10.1007/s43034-022-00167-8