An injective-type norm and integral bilinear forms defined by sequence classes

TL;DR

This paper introduces a new injective-type norm on tensor products based on sequence classes, explores its duality, and defines related integral bilinear forms with tensor characterizations for sequence spaces.

Contribution

It presents a novel injective-type norm on tensor products using sequence classes and studies its duality and associated bilinear forms.

Findings

Defined a new injective-type norm on tensor products.

Studied the duality properties of the norm.

Characterized integral bilinear forms and tensor structures for sequence spaces.

Abstract

In this work we define a class of injective-type norm on tensor products through the environment of sequence classes. Examples and results on this norm will be presented and the duality is studied in this context. As a byproduct, we present the definition of the associated integral-type bilinear forms and also a tensor characterization for a class of sequence spaces.