‎Some notes on subspace convex-cyclicity

Authors

  • Meysam Asadipour Department of Mathematics, College of Sciences‎, Yasouj University, Yasouj, Iran

Keywords:

Hypercyclicity‎, ‎Convex hull‎, ‎Subspace convex-cyclic operators

Abstract

‎A bounded linear operator $T$ on Banach space $X$ is subspace convex-cyclic for a subspace $M$‎

‎if there exists a vector $x \in M$ such that $Co(orb(T‎, ‎x)) \cap M$ is dense in $M$‎.

‎We construct examples of subspace convex-cyclic operator that is not convex-cyclic‎.

‎In particular‎, ‎we prove that every convex-cyclic operator on the separable Banach space $X$‎

‎is a subspace convex-cyclic operator for some pure subspace $M$ of $X$‎.‎

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Published

2021-08-07

Issue

Vol. 16

Section

Vol. 16, No. 5, (2022)

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