A NOTE ON ∗-PARANORMAL OPERATORS AND RELATED CLASSES OF OPERATORS

Title & Authors
A NOTE ON ∗-PARANORMAL OPERATORS AND RELATED CLASSES OF OPERATORS
Tanahashi, Kotoro; Uchiyama, Atsushi;

Abstract
We shall show that the Riesz idempotent $\small{E_{\lambda}}$ of every *-paranormal operator T on a complex Hilbert space H with respect to each isolated point $\small{{\lambda}}$ of its spectrum $\small{{\sigma}(T)}$ is self-adjoint and satisfies $\small{E_{\lambda}\mathcal{H}=ker(T-{\lambda})= ker(T-{\lambda})^*}$. Moreover, Weyl's theorem holds for *-paranormal operators and more general for operators T satisfying the norm condition $\small{||Tx||^n{\leq}||T^nx||\,||x||^{n-1}}$ for all $\small{x{\in}\mathcal{H}}$. Finally, for this more general class of operators we find a sufficient condition such that $\small{E_{\lambda}\mathcal{H}=ker(T-{\lambda})= ker(T-{\lambda})^*}$ holds.
Keywords
*-paranormal;k-paranormal;normaloid;the single valued extension property;Weyl's theorem;
Language
English
Cited by
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Finite Operators and Weyl Type Theorems for Quasi-*-n-Paranormal Operators,;;

Kyungpook mathematical journal, 2015. vol.55. 4, pp.885-892
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ON n-*-PARANORMAL OPERATORS, Communications of the Korean Mathematical Society, 2016, 31, 3, 549
2.
On k-quasi- $$*$$ ∗ -paranormal operators, Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 2016, 110, 2, 655
3.
New results on common properties of the products AC and BA, Journal of Mathematical Analysis and Applications, 2015, 427, 2, 830
4.
Riesz idempotent of ( n , k )-quasi-*-paranormal operators, Acta Mathematica Scientia, 2016, 36, 5, 1487
5.
Finite Operators and Weyl Type Theorems for Quasi-*-n-Paranormal Operators, Kyungpook mathematical journal, 2015, 55, 4, 885
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