Non-Archimedean Unitary Operators

TL;DR

This paper introduces a subclass of normal operators on Banach spaces over non-Archimedean fields that behave similarly to unitary operators, including an analog of Stone's theorem for one-parameter groups.

Contribution

It defines a new subclass of operators in non-Archimedean Banach spaces and proves an analog of Stone's theorem for these operators.

Findings

Defined a subclass of normal operators resembling unitary operators

Proved an analog of Stone's theorem in the non-Archimedean setting

Established properties of one-parameter groups of these operators

Abstract

We describe a subclass of the class of normal operators on Banach spaces over non-Archimedean fields (A. N. Kochubei, J. Math. Phys. 51 (2010), article 023526) consisting of operators whose properties resemble those of unitary operators. In particular, an analog of Stone's theorem about one-parameter groups of unitary operators is proved.