Zippin's embedding theorem and amalgamations of classes of Banach spaces

TL;DR

This paper presents an isometric version of a known result, showing that certain classes of Banach spaces with specific duality and reflexivity properties are strongly bounded, extending previous work by Dodos and Ferenczi.

Contribution

It provides an isometric version of the strong boundedness results for classes of Banach spaces with separable duals and reflexivity, enhancing the understanding of their structural properties.

Findings

Established an isometric version of strong boundedness for Banach space classes.

Extended previous results by Dodos and Ferenczi to isometric settings.

Contributed to the theory of Banach space classifications and embeddings.

Abstract

It was proved by Dodos and Ferenczi that the classes of Banach spaces with a separable dual and of separable reflexive Banach spaces are strongly bounded. In this note, we provide an isometric version of this result.