On subspaces diskcyclicity

TL;DR

This paper introduces the concept of subspace-diskcyclic operators, explores their properties, and establishes criteria, revealing distinctions from diskcyclicity and demonstrating their existence in finite-dimensional spaces.

Contribution

It defines subspace-diskcyclicity, provides a criterion for it, and shows that such operators can exist without being diskcyclic or subspace-hypercyclic, including in finite-dimensional spaces.

Findings

Subspace-diskcyclicity does not imply diskcyclicity.

A subspace-diskcyclic criterion is established.

Every finite-dimensional separable Hilbert space supports a subspace-diskcyclic operator.

Abstract

In this paper, we define and study subspace-diskcyclic operators. We show that subspace-diskcyclicity does not imply to diskcyclicity. We establish a subspace-diskcyclic criterion and use it to find a subspace-diskcyclic operator that is not subspace-hypercyclic for any subspaces. Also, we show that the inverse of invertible subspace-diskcyclic operators do not need to be subspace-diskcyclic for any subspaces. Finally, we prove that every finite-dimensional separable Hilbert space over the complex field supports a subspace-diskcyclic operator.