On Bernstein classes of quasianalytic maps

TL;DR

This paper investigates the structure of well approximable elements in tensor products of Banach spaces, extending classical quasianalytic concepts and establishing new theorems and estimates for these families.

Contribution

It introduces analogs of Bernstein and Beurling quasianalytic classes in tensor product settings and proves variants of classical theorems for these classes.

Findings

Proves variants of Mazurkiewicz and Markushevich theorems for these classes.

Estimates the massivity of graphs and level sets of Banach-valued maps.

Extends classical quasianalytic results to tensor product frameworks.

Abstract

We study the structure of families of well approximable elements of tensor products of Banach spaces including analogs of the classical quasianalytic classes in the sense of Bernstein and Beurling. As in the case of quasianalytic functions, we prove for members of these families variants of the Mazurkiewicz and Markushevich theorems and in some particular cases, if such elements are Banach-valued continuous maps on a compact metric space, estimate massivity of their graphs and level sets.