• Home
  • Browse
    • Current Issue
    • By Issue
    • By Author
    • By Subject
    • Author Index
    • Keyword Index
  • Journal Info
    • About Journal
    • Aims and Scope
    • Editorial Board
    • Publication Ethics
    • Indexing and Abstracting
    • Related Links
    • FAQ
    • Peer Review Process
    • News
  • Guide for Authors
  • Submit Manuscript
  • Reviewers
  • Contact Us
 
  • Login
  • Register
Home Articles List Article Information
  • Save Records
  • |
  • Printable Version
  • |
  • Recommend
  • |
  • How to cite Export to
    RIS EndNote BibTeX APA MLA Harvard Vancouver
  • |
  • Share Share
    CiteULike Mendeley Facebook Google LinkedIn Twitter
Advances in Operator Theory
arrow Articles in Press
arrow Current Issue
Journal Archive
Volume Volume 4 (2019)
Issue Issue 2
Issue Issue 1
Volume Volume 3 (2018)
Volume Volume 2 (2017)
Volume Volume 1 (2016)
Sahoo, S., Das, N., Mishra, D. (2019). Numerical radius inequalities for operator matrices. Advances in Operator Theory, 4(1), 197-214. doi: 10.15352/aot.1804-1359
Satyajit Sahoo; Namita Das; Debasisha Mishra. "Numerical radius inequalities for operator matrices". Advances in Operator Theory, 4, 1, 2019, 197-214. doi: 10.15352/aot.1804-1359
Sahoo, S., Das, N., Mishra, D. (2019). 'Numerical radius inequalities for operator matrices', Advances in Operator Theory, 4(1), pp. 197-214. doi: 10.15352/aot.1804-1359
Sahoo, S., Das, N., Mishra, D. Numerical radius inequalities for operator matrices. Advances in Operator Theory, 2019; 4(1): 197-214. doi: 10.15352/aot.1804-1359

Numerical radius inequalities for operator matrices

Article 9, Volume 4, Issue 1 - Serial Number 11, Winter 2019, Page 197-214  XML PDF (132.2 K)
Document Type: Special issue: Trends in Operators on Banach Spaces
DOI: 10.15352/aot.1804-1359
Authors
Satyajit Sahoo1; Namita Das1; Debasisha Mishra email 2
1P.G. Department of Mathematics, Utkal University, Vanivihar, Bhubaneswar-751004, India.
2National Institute of Technology Raipur, India
Receive Date: 30 April 2018,  Revise Date: 16 June 2018,  Accept Date: 19 June 2018 
Abstract
Several numerical radius inequalities for operator matrices are
proved by generalizing earlier inequalities. In particular,  the
following inequalities are obtained:
if $n$ is even, \\
$$2w(T) \leq max\{\| A_1 \|, \| A_2 \|,\ldots, \| A_n \|\}+\frac{1}{2}\displaystyle\sum_{k=0}^{n-1} \|~     |A_{n-k}|^{t}|A_{k+1}^{*}|^{1-t} \|$$\\
and if $n$ is odd, \\
$$2w(T) \leq max\{\| A_1 \|,\| A_2 \|,\ldots,\| A_n \|\}+ w\bigg(\widetilde{A}_{(\frac{n+1}{2})t}\bigg)+ \frac{1}{2}\displaystyle\sum_{k=0}^{n-1} \|~     |A_{n-k}|^{t}|A_{k+1}^{*}|^{1-t} \|$$
for all $t\in [0, 1]$, $ A_i$'s are bounded linear operators on the
Hilbert space $\mathcal{H}$, and $ T=\begin{bmatrix}
{\bigzero}   &   &   A_1\\
&   \hspace{4mm}A_2 & \\
& \hspace{-8mm}\reflectbox{$\ddots$} &  \\
A_n   & & {\!\!\bigzero}
\end{bmatrix}$.
Keywords
Spectral radius; Numerical radius; Operator matrix; Aluthge transform; polar decomposition
Main Subjects
47. Operator Theory (Main Subject)
Statistics
Article View: 213
PDF Download: 285
Home | Glossary | News | Aims and Scope | Sitemap
Top Top

Journal Management System. Designed by sinaweb.