Isometries and Hermitian Operators on Zygmund spaces

TL;DR

This paper characterizes the isometries and hermitian operators on subspaces of the little Zygmund space, showing their structure as integral operators and their boundedness.

Contribution

It provides a complete characterization of isometries and hermitian operators on subspaces of the little Zygmund space, including their representation and boundedness.

Findings

Isometries are surjective and represented as integral operators.

All hermitian operators are bounded.

Provides structural insights into operators on Zygmund spaces.

Abstract

In this paper we characterize the isometries of subspaces of the little Zygmund space. We show that the isometries of these spaces are surjective and represented as integral operators. We also show that all hermitian operators on these settings are bounded.