Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

The behaviour of quasi-linear maps on $C(K)$-spaces

Félix Cabello Sánchez, Jesús M. F. Castillo, Alberto Salguero-Alarcón

Abstract

In this paper we combine topological and functional analysis methods to prove that a non-locally trivial quasi-linear map defined on a $C(K)$ must be nontrivial on a subspace isomorphic to $c_0$. We conclude the paper with a few examples showing that the result is optimal, and providing an application to the existence of nontrivial twisted sums of $\ell_1$ and $c_0$.

The behaviour of quasi-linear maps on $C(K)$-spaces

Abstract

In this paper we combine topological and functional analysis methods to prove that a non-locally trivial quasi-linear map defined on a must be nontrivial on a subspace isomorphic to . We conclude the paper with a few examples showing that the result is optimal, and providing an application to the existence of nontrivial twisted sums of and .
Paper Structure (3 sections, 4 theorems, 7 equations)

This paper contains 3 sections, 4 theorems, 7 equations.

Table of Contents

  1. Introduction and preliminaries
  2. A dichotomy for $C(K)$ spaces
  3. Consequences and applications

Key Result

Theorem 2.1

A quasi-linear map $\Omega: C(K) \to Y$ either is locally trivial or admits a subspace isomorphic to $c_0$ on which its restriction is not locally trivial.

Theorems & Definitions (10)

  • Definition 1
  • Theorem 2.1
  • Lemma 2.2
  • proof
  • proof
  • proof
  • Lemma 2.3
  • proof
  • proof
  • Corollary 2.4