On notions of expansivity for operators on locally convex spaces

Revista de la Real Academia de Ciencias Exactas Físicas y Naturales Serie A Matemáticas 2026 Open access

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Authors: Nilson C. Bernardes, Félix Martı́nez-Giménez, F. Ródenas
DOI: 10.1007/s13398-026-01840-6
Cited by: 1
References: 20

Abstract

Abstract We extend the concept of average expansivity for operators on Banach spaces to operators on arbitrary locally convex spaces. We obtain complete characterizations of the average expansive weighted shifts on Fréchet sequence spaces. Moreover, we give a partial answer to a problem proposed by Bernardes et al. (J Funct Anal 288(2):51, Paper No. 110696, 2025), by obtaining complete characterizations of the uniformly expansive weighted shifts on Köthe sequence spaces. Some general properties of the various concepts of expansivity in linear dynamics and several concrete examples are also presented.

Fields of Study & Subjects

Nonlinear Differential Equations Analysis Advanced Banach Space Theory Fixed Point Theorems Analysis

Publication details

Journal / source
Revista de la Real Academia de Ciencias Exactas Físicas y Naturales Serie A Matemáticas
Publisher
Springer Science and Business Media LLC
Volume
120
Issue
2
Publication date
5 March 2026
Language
EN