Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Inequalities on the essential joint and essential generalized spectral radius

B. Lins, A. Peperko

Abstract

We prove new inequalities for the essential generalized and the essential joint spectral radius of Hadamard (Schur) weighted geometric means of bounded sets of infinite nonnegative matrices that define operators on suitable Banach sequence spaces and of bounded sets of positive kernel operators on $L^2$. To our knowledge the obtained inequalities are new even in the case of singelton sets.

Inequalities on the essential joint and essential generalized spectral radius

Abstract

We prove new inequalities for the essential generalized and the essential joint spectral radius of Hadamard (Schur) weighted geometric means of bounded sets of infinite nonnegative matrices that define operators on suitable Banach sequence spaces and of bounded sets of positive kernel operators on . To our knowledge the obtained inequalities are new even in the case of singelton sets.
Paper Structure (5 sections, 35 theorems, 145 equations)

This paper contains 5 sections, 35 theorems, 145 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. New inequalities for the Haussdorf measure of noncompactness and essential radius
  4. Further results
  5. Further results on $L^2(X,\mu)$

Key Result

Theorem 2.1

Let $\{A_{i j}\}_{i=1, j=1}^{k, m}$ be positive kernel operators on a Banach function space $L$ and $\alpha _1$, $\alpha _2$,..., $\alpha _m$ positive numbers. (i) If $\sum_{j=1}^{m} \alpha _j = 1$, then the positive kernel operator satisfies the following inequalities If, in addition, $L$ and $L^*$ have order continuous norms, then (ii) If $L\in\mathcal{L}$, $\sum_{j=1}^{m} \alpha _j\ge 1$ and

Theorems & Definitions (49)

  • Theorem 2.1
  • Theorem 2.2
  • Theorem 2.3
  • Theorem 2.4
  • Lemma 3.1
  • proof
  • Theorem 3.2
  • proof
  • Remark 3.3
  • Theorem 3.4
  • ...and 39 more