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2013 Weyl type theorem and spectrum for $(p,k)$-quasiposinormal operators
D. Senthilkumar, D. Kiruthika , P. Maheswari Naik
Banach J. Math. Anal. 7(2): 30-41 (2013). DOI: 10.15352/bjma/1363784221

Abstract

Let $T$ be a $(p,k)$-quasiposinormal operator on a complex Hilbert space $\mathcal{H}$, i.e $T^{*k}(c^{2}(T^{*} T)^{p}-(T T^{*})^{p})T^{k} \geq 0$ for a positive integer $p \in (0,1]$, some $c > 0$ and a positive integer $k$. In this paper, we prove that the spectral mapping theorem for Weyl spectrum holds for $(p, k)$ - quasiposinormal operators. We show that the Weyl type theorems holds for $(p,k)$- quasiposinormal. We prove that if $T^{*}$ is $(p,k)$-quasiposinormal, then generalized $a$-Weyl's theorem holds for $T$. Also we prove that $\sigma_{jp}(T)-\{0\} = \sigma_{ap}(T)-\{0\}$ holds for $(p,k)$-quasiposinormal operator.

Citation

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D. Senthilkumar. D. Kiruthika . P. Maheswari Naik . "Weyl type theorem and spectrum for $(p,k)$-quasiposinormal operators." Banach J. Math. Anal. 7 (2) 30 - 41, 2013. https://doi.org/10.15352/bjma/1363784221

Information

Published: 2013
First available in Project Euclid: 20 March 2013

zbMATH: 1291.47018
MathSciNet: MR3039937
Digital Object Identifier: 10.15352/bjma/1363784221

Subjects:
Primary: 47A10
Secondary: 47B20

Keywords: $(p, k)$-quasiposinormal operator , $p$-posinormal , B-Fredholm , generalized $a$-Weyl's theorem

Rights: Copyright © 2013 Tusi Mathematical Research Group

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Vol.7 • No. 2 • 2013
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