Isometries and Hermitian operators on $\mathcal{B}_0(\triangle, E)$

TL;DR

This paper characterizes the structure of surjective isometries, hermitian operators, and bi-circular projections on vector-valued little Bloch spaces with specific geometric properties.

Contribution

It provides a detailed description of these operators on vector-valued little Bloch spaces with strictly convex and smooth Banach space range.

Findings

Surjective linear isometries are characterized for the space.

Hermitian operators on these spaces are described.

Generalized bi-circular projections are identified and analyzed.

Abstract

In this paper we describe the surjective linear isometries on a vector valued little Bloch space with range space a strictly convex and smooth complex Banach space. We also describe the hermitian operators and the generalized bi-circular projections supported by these spaces.