Disjoint hypercyclic weighted pseudo-shift operators generated by different shifts

TL;DR

This paper characterizes disjoint hypercyclic and supercyclic weighted pseudo-shift operators on Banach sequence spaces, linking their properties to weights, basis, and shift mappings, with applications to weighted spaces on trees and operator shifts.

Contribution

It provides a comprehensive characterization of disjoint hypercyclicity and supercyclicity for weighted pseudo-shift operators, extending to specific cases like tree-based weighted spaces and operator shifts.

Findings

Characterization of disjoint hypercyclic and supercyclic weighted pseudo-shift operators.

Application to shifts on weighted $L^p$ spaces of directed trees.

Analysis of operator weighted shifts on $\, ext{ell}^2( ext{Z}, ext{K})$.

Abstract

Let $I$ be a countably infinite index set, and let $X$ be a Banach sequence space over $I.$ In this article, we characterize disjoint hypercyclic and supercyclic weighted pseudo-shift operators on $X$ in terms of the weights, the OP-basis, and the shift mappings on $I.$ Also, the shifts on weighted $L^p$ spaces of a directed tree and the operator weighted shifts on $\ell^2(\mathbb{Z,\mathcal{K}})$ are investigated as special cases.