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 $E_{\lambda}\mathcal{H} Keywords *-paranormal;k-paranormal;normaloid;the single valued extension property;Weyl`s theorem; Language English Cited by 1. Finite Operators and Weyl Type Theorems for Quasi-*-n-Paranormal Operators,;; Kyungpook mathematical journal, 2015. vol.55. 4, pp.885-892 2. ON n-*-PARANORMAL OPERATORS,; 대한수학회논문집, 2016. vol.31. 3, pp.549-565 1. 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 References 1. S. C. Arora and J. K. Thukral, On a class of operators, Glas. Mat. Ser. III 21(41) (1986), no. 2, 381-386. 2. B. Arun, On k-paranormal operators, Bull. Math. Soc. Sci. Math. Roumanie (N.S.) 20(68) (1976), no. 1-2, 37-39. 3. B. P. Duggal and C. S. Kubrusly, Quasi-similar k-paranormal operators, Oper. Matrices 5 (2011), no. 3, 417-423. 4. T. Furuta, On the class of paranormal operators, Proc. Japan Acad. Ser. A Math. Sci. 43 (1967), 594-598. 5. Y. M. Han and A. H. Kim, A note on ∗-paranormal operators, Integral Equations Operator Theory 49 (2004), no. 4, 435-444. 6. V. Istratescu, T. Saito, and T. Yoshino, On a class of operators, Tohoku Math. J. (2) 18 (1966), 410-413. 7. C. S. Kubrusly and B. P. Duggal, A note on k-paranormal operators, Oper. Matrices 4 (2010), no. 2, 213-223. 8. S. M. Patel, Contributions to the study of spectraloid operators, Ph. D. Thesis, Delhi University 1974. 9. A. Uchiyama, On the isolated point of the spectrum of paranormal operators, Integral Equations Operator Theory 55 (2006), no. 1, 145-151. 10. A. Uchiyama and K. Tanahashi, Bishop's property (${\beta}\$) for paranormal operators, Oper. Matrices 3 (2009), no. 4, 517-524.