## Banach Journal of Mathematical Analysis

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

#### Abstract

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

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

Dates
First available in Project Euclid: 14 August 2011

https://projecteuclid.org/euclid.bjma/1313362977

Digital Object Identifier
doi:10.15352/bjma/1313362977

Mathematical Reviews number (MathSciNet)
MR2738517

Zentralblatt MATH identifier
1221.47038

#### Citation

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. https://projecteuclid.org/euclid.bjma/1313362977