Diskcyclicity of sets of operators and applications

Mohamed Amouch; Otmane Benchiheb

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arXiv · 1905.04507

Diskcyclicity of sets of operators and applications

Mohamed Amouch·Otmane Benchiheb

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Abstract

In this paper, we extend the notion of diskcyclicity and disk transitivity of a single operator to a subset of $\mathcal{B}(X)$. We establish a diskcyclicity criterion and we give the relationship between this criterion and the diskcyclicity. As applications, we study the diskcyclicty of $C_0$-semigroups and $C$-regularized groups of operators. We show that a diskcyclic $C_0$-semigroup exists on a complex topological vector space $X$ if and only if dim$(X)=1$ or dim$(X)=\infty$ and we prove that diskcyclicity and disk transitivity of a $C_0$-semigroups and $C$-regularized groups are equivalent.

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Mohamed Amouch, Otmane Benchiheb. 2019-05-11. Diskcyclicity of sets of operators and applications. https://arxiv.org/abs/1905.04507

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