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Upper bounds of numerical radius and $a$-numerical radius in $\mathcal{C}^*$-algebra setting using Orlicz functions

Saikat Mahapatra, Riddhick Birbonshi, Arnab Patra

Abstract

In this paper, several significant upper bounds for the numerical radius and $a$-numerical radius of an element in a $\mathcal{C}^*$-algebra are obtained using Orlicz functions. Many well-known results are obtained from our findings, depending on specific choices of Orlicz functions.

Upper bounds of numerical radius and $a$-numerical radius in $\mathcal{C}^*$-algebra setting using Orlicz functions

Abstract

In this paper, several significant upper bounds for the numerical radius and -numerical radius of an element in a -algebra are obtained using Orlicz functions. Many well-known results are obtained from our findings, depending on specific choices of Orlicz functions.

Paper Structure

This paper contains 2 sections, 32 theorems, 59 equations.

Table of Contents

  1. Introduction and preliminaries
  2. Main Result

Key Result

Lemma 2.1

blackadar2006operator Let $g$ be a non-zero positive linear functional on a $\mathcal{C}^*$-algebra $\mathcal{A}$. Then $|g(x^*y)|^2\le g(x^*x)g(y^*y)$ for all $x,y\in \mathcal{A}$.

Theorems & Definitions (68)

  • Lemma 2.1
  • Lemma 2.2
  • Lemma 2.3
  • Corollary 2.4
  • proof
  • Lemma 2.5
  • proof
  • Corollary 2.6
  • proof
  • Lemma 2.7
  • ...and 58 more