Vector-valued Eidelheit sequences and the non B-completeness of tensor products

TL;DR

This paper introduces vector-valued Eidelheit sequences, generalizes a classical theorem, and provides criteria for the non B-completeness of completed tensor products, advancing the understanding of tensor product topologies.

Contribution

It generalizes Eidelheit's classical theorem to vector-valued sequences and applies this to characterize non B-completeness in tensor products.

Findings

Generalization of Eidelheit's theorem to vector-valued sequences

Criteria for non B-completeness of tensor products

Enhanced understanding of tensor product topologies

Abstract

We introduce vector-valued Eidelheit sequences and obtain a characterization that generalizes Eidelheit's classical theorem (Studia Math. 6 (1936), 139-148). As an application, we discuss criteria for non $B$-completeness of completed tensor products.