On Notions of Expansivity for Operators on Locally Convex Spaces

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 Fr\'echet sequence spaces. Moreover, we give a partial answer to a problem proposed by Bernardes et al. in J. Funct. Anal. 288 (2025), Paper No. 110696, by obtaining complete characterizations of the uniformly expansive weighted shifts on K\"othe sequence spaces. Some general properties of the various concepts of expansivity in linear dynamics and several concrete examples are also presented.

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