Furstenberg theorem for frequently hypercyclic operators

TL;DR

This paper establishes that for frequently hypercyclic operators, the property extends from the direct sum of two to any finite direct sum, revealing a structural stability in their hypercyclicity behavior.

Contribution

It proves that if the direct sum of two frequently hypercyclic operators is frequently hypercyclic, then all higher direct sums share this property, a new insight into operator hypercyclicity.

Findings

If T⊕T is frequently hypercyclic, then T⊕...⊕T is also frequently hypercyclic for all finite sums.

The result links the hypercyclicity of a pairwise sum to all higher sums.

Provides a new criterion for frequent hypercyclicity in operator theory.

Abstract

In this paper, we show that if the direct sum $T\oplus T$ of frequently hypercyclic operators is frequently hypercyclic, then every higher direct sum $T\oplus\cdots\oplus T$ is also frequently hypercyclic.