Banach Journal of Mathematical Analysis

Weyl's theorem for algebraically absolute-(p,r)-paranormal operators

P. Maheswari Naik and D. Senthilkumar

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An operator $T \in B(H)$ is said to be absolute-$(p, r)$-paranormal if $\| |T|^{p} |T^{*}|^{r} x \|^{r} \|x\| \geq \| |T^{*}|^{r} x\|^{p + r}$ for all $x \in H$ and for positive real number $p > 0$ and $r > 0$, where $T=U |T|$ is the polar decomposition of $T$. In this paper, we discuss some properties of absolute-$(p, r)$-paranormal operators and show that Weyl's theorem holds for algebraically absolute-$(p, r)$-paranormal operators.

Article information

Banach J. Math. Anal., Volume 5, Number 1 (2011), 29-37.

First available in Project Euclid: 14 August 2011

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 47A13: Several-variable operator theory (spectral, Fredholm, etc.)
Secondary: 47A30: Norms (inequalities, more than one norm, etc.) 47B06: Riesz operators; eigenvalue distributions; approximation numbers, s- numbers, Kolmogorov numbers, entropy numbers, etc. of operators

absolute-(p,r)-paranormal operator nilpotent, normaloid Riesz idempotent single valued extension property stable index Drazin invertible Drazin spectrum


Senthilkumar, D.; Maheswari Naik, P. Weyl's theorem for algebraically absolute-(p,r)-paranormal operators. Banach J. Math. Anal. 5 (2011), no. 1, 29--37. doi:10.15352/bjma/1313362977.

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