Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

$q$-Numerical Radius Estimates in Semi-Hilbertian Spaces and Their Relations with Matrix Means for Sectorial Matrices

Jyoti Rani

Abstract

In this paper, the $q$-numerical radius of operators in semi-Hilbertian spaces is studied. New characterizations are established, and sharp upper and lower bounds for the $q$-numerical radius are derived. Moreover, several inequalities involving operator monotone functions and matrix means for the $q$-numerical radius of sectorial matrices are obtained.

$q$-Numerical Radius Estimates in Semi-Hilbertian Spaces and Their Relations with Matrix Means for Sectorial Matrices

Abstract

In this paper, the -numerical radius of operators in semi-Hilbertian spaces is studied. New characterizations are established, and sharp upper and lower bounds for the -numerical radius are derived. Moreover, several inequalities involving operator monotone functions and matrix means for the -numerical radius of sectorial matrices are obtained.
Paper Structure (3 sections, 19 theorems, 66 equations)

This paper contains 3 sections, 19 theorems, 66 equations.

Table of Contents

  1. Introduction and Preliminaries
  2. $A$-$q$-Numerical Radius Estimations
  3. Realtion between $q$-Numerical Range and Matrix Means for Sectorial Matrices

Key Result

Lemma 1.1

bedrani2021positive If $A \in \prod_{s,\alpha}^n$, $f \in \mathcal{F}$, we have

Theorems & Definitions (38)

  • Definition 1.1
  • Lemma 1.1
  • Lemma 1.2
  • Lemma 2.1
  • Theorem 2.1
  • proof
  • Remark 2.1
  • Theorem 2.2
  • proof
  • Remark 2.2
  • ...and 28 more