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Lower and upper bounds of joint $(f,δ)$-numerical radius functions

Zameddin I. Ismailov, Sergei Silvestrov, Pembe Ipek Al

Abstract

In this study, the classical results on the joint numerical radius for $n$-tuples of Hilbert space operators are extended to the setting of the joint $(f,δ)$-numerical radius. New and diverse contributions to this area are provided, including novel estimates for the lower and upper bounds of the $(f,δ)$-numerical radius in the context of sectorial operators.

Lower and upper bounds of joint $(f,δ)$-numerical radius functions

Abstract

In this study, the classical results on the joint numerical radius for -tuples of Hilbert space operators are extended to the setting of the joint -numerical radius. New and diverse contributions to this area are provided, including novel estimates for the lower and upper bounds of the -numerical radius in the context of sectorial operators.
Paper Structure (3 sections, 27 theorems, 106 equations)

This paper contains 3 sections, 27 theorems, 106 equations.

Table of Contents

  1. Introduction
  2. Joint (f,delta)-numerical radius of n-tuples of operators
  3. Sectorial case of coordinate operators

Key Result

Theorem 1

Let $\mathbb{A} = (A_{1}, \ldots, A_{n}), \ \mathbb{B} = (B_{1}, \ldots, B_{n}) \in \mathfrak{B}^{n}(\mathcal{H})$.

Theorems & Definitions (54)

  • Definition 1
  • Example 1: Pauli tuple
  • Definition 2: Stampfli1970
  • Definition 3
  • Definition 4
  • Definition 5: Alomari2024
  • Definition 6
  • Example 2
  • Definition 7
  • Theorem 1
  • ...and 44 more