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A new collection of $n-$tuple operator inequalities

Zameddin I. Ismailov, Pembe Ipek Al, Hamid Reza Moradi, Mohammad Sababheh

Abstract

In this paper, we present several new bounds for the norm and numerical radius of sums of Hilbert space operators. The obtained bounds form a new collection that enriches our understanding of these bounds. We compare our bounds with the existing literature using examples that demonstrate, in general, how our results are incomparable with the known bounds. Of particular interest are the treatment of the triangle inequality, the numerical radius of operator matrices, and singular value bounds for sums of operators.

A new collection of $n-$tuple operator inequalities

Abstract

In this paper, we present several new bounds for the norm and numerical radius of sums of Hilbert space operators. The obtained bounds form a new collection that enriches our understanding of these bounds. We compare our bounds with the existing literature using examples that demonstrate, in general, how our results are incomparable with the known bounds. Of particular interest are the treatment of the triangle inequality, the numerical radius of operator matrices, and singular value bounds for sums of operators.
Paper Structure (2 sections, 7 theorems, 63 equations)

This paper contains 2 sections, 7 theorems, 63 equations.

Table of Contents

  1. Introduction
  2. Main results

Key Result

Lemma 1.1

Let $T\in\mathbb{K}(\mathbb{H})$. Then for $j=1,2,\ldots,$

Theorems & Definitions (21)

  • Lemma 1.1
  • Theorem 2.1
  • proof
  • Remark 2.1
  • Remark 2.2
  • Theorem 2.2
  • proof
  • Remark 2.3
  • Remark 2.4
  • Remark 2.5
  • ...and 11 more