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Decomposition of the set of Banach limits into discrete and continuous subsets

Nikolai Avdeev, Evgenii Semenov, Alexandr Usachev, Roman Zvolinskii

Abstract

The aim of this work is to describe subsets of Banach limits in terms of a certain functional characteristic. We compute radii and cardinalities for some of these subsets.

Decomposition of the set of Banach limits into discrete and continuous subsets

Abstract

The aim of this work is to describe subsets of Banach limits in terms of a certain functional characteristic. We compute radii and cardinalities for some of these subsets.
Paper Structure (4 sections, 17 theorems, 71 equations)

This paper contains 4 sections, 17 theorems, 71 equations.

Table of Contents

  1. Introduction and preliminaries
  2. A functional characteristic
  3. Cesàro invariant Banach limits
  4. Some cardinalities

Key Result

Theorem 2.1

A Banach limit $B$ belongs to the set $B_c$ if and only if the function $\gamma(B, \cdot)$ is continuous.

Theorems & Definitions (32)

  • Definition 1.1
  • Theorem 2.1
  • proof
  • Theorem 2.2
  • proof
  • Theorem 2.3
  • proof
  • Corollary 2.4
  • Remark 2.5
  • Lemma 3.1
  • ...and 22 more