Dynamical properties and some classes of non-porous subsets
Stefan Ivkovic, Serap Oztop, Seyyed Mohammad Tabatabaie
TL;DR
This paper introduces new classes of non-porous sets in Lebesgue spaces and investigates the linear dynamics of weighted translation operators, showing the non-porosity of non-hypercyclic vectors.
Contribution
It defines several classes of non-{ extsigma}-porous subsets and analyzes the non-porosity of non-hypercyclic vectors in weighted translation operators.
Findings
Non-{ extsigma}-porous sets are introduced in Lebesgue spaces.
The set of non-hypercyclic vectors is not { extsigma}-porous.
New classes of non-porous subsets are characterized.
Abstract
In this paper, we introduce several classes of non-{\sigma}-porous subsets of a general Lebesgue space. Also, we study some linear dynamics of operators and show that the set of all non-hypercyclic vectors of a sequence of weighted translation operators on Lp-spaces is not {\sigma}-porous.
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Taxonomy
TopicsApproximation Theory and Sequence Spaces · Fixed Point Theorems Analysis · Advanced Banach Space Theory