Abstract
In this paper, we introduce the notion of $m$-quasi-$n$-power-totally-$(\alpha,\beta)$-normal operators on a Hilbert space $\mathscr{H}$ as : An operator $\mathcal{L}$ is called $m$-quasi-$n$-power-totally-$(\alpha,\beta)$-normal $(0\leq \alpha \leq 1 \leq \beta)$ if
\begin{align*}
\alpha^{2}\mathcal{L}^{m*}(\mathcal{L}-\lambda)^{*}(\mathcal{L}-\lambda )^{n}\mathcal{L}^{m}& \leq \mathcal{L}^{m*}(\mathcal{L}-\lambda)^{n}(\mathcal{L}-\lambda)^{*}\mathcal{L}^{m}\\ &\leq \beta^{2} \mathcal{L}^{m*}(\mathcal{L}-\lambda)^{*}(\mathcal{L}-\lambda )^{n}\mathcal{L}^{m}
\end{align*}
for natural numbers $m$ and $n$ and for all $\lambda \in \mathbb{C}$. This paper aims to study several properties of $m$-quasi-$n$-power-totally-$(\alpha,\beta)$-normal operators.
Key words: $(\alpha,\beta)$-normal, $m$-quasi-totally-$(\alpha,\beta)$-normal, $m$-quasi-$n$-power-totally-$(\alpha,\beta)$-normal.
Full Text
Article Information
| Title | On $m$-quasi-$n$-power-totally-$(\alpha,\beta)$-normal operators |
| Source | Methods Funct. Anal. Topology, Vol. 31 (2025), no. 3, 247-260 |
| DOI | 10.31392/MFAT-npu26_3.2025.08 |
| Milestones | Received 18/01/2025; Revised 03/06/2025 |
| Copyright | The Author(s) 2025 (CC BY-SA) |
Authors Information
Pradeep Radhakrishnan
Department of Mathematics, Sri Ramakrishna Engineering College, Coimbatore-641 022,Tamil Nadu, India
Sid Ahmed Ould Ahmed Mahmoud
Mathematics Department, College of Science, Jouf University, Sakaka P.O.Box 2014. Saudi Arabia
P. Maheswari Naik
Department of Mathematics, Sri Ramakrishna Engineering College, Coimbatore-641 022,Tamil Nadu, India
Citation Example
Pradeep Radhakrishnan, Sid Ahmed Ould Ahmed Mahmoud, and P. Maheswari Naik, On $m$-quasi-$n$-power-totally-$(\alpha,\beta)$-normal operators, Methods Funct. Anal. Topology 31
(2025), no. 3, 247-260.
BibTex
@article {MFAT2128,
AUTHOR = {Pradeep Radhakrishnan and Sid Ahmed Ould Ahmed Mahmoud and P. Maheswari Naik},
TITLE = {On $m$-quasi-$n$-power-totally-$(\alpha,\beta)$-normal operators},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {31},
YEAR = {2025},
NUMBER = {3},
PAGES = {247-260},
ISSN = {1029-3531},
DOI = {10.31392/MFAT-npu26_3.2025.08},
URL = {https://mfat.imath.kiev.ua/article/?id=2128},
}
