Non-Archimedean Shift Operators

TL;DR

This paper explores non-Archimedean analogs of classical shift operators, developing functional models that reveal both similarities and differences from traditional operator theory.

Contribution

It introduces non-Archimedean shift operators and constructs their functional models, expanding the understanding of operator theory in non-Archimedean settings.

Findings

Non-Archimedean shift operators are successfully modeled.

Functional models exhibit unique features compared to classical cases.

The study highlights both commonalities and differences with classical operator theory.

Abstract

We introduce and study non-Archimedean analogs of the operators of unilateral shift and backward shift playing crucial roles in the classical theory of nonselfadjoint operators. In particular, we find various functional models of these operators having both common and different features compared to their classical counterparts.