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

Jamilson R. Campos, Lucas Nascimento, Luiz Felipe de Pinho Sousa

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.

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

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.

Paper Structure

This paper contains 5 sections, 11 theorems, 66 equations.

Table of Contents

  1. Introduction
  2. Dual classes
  3. Injective-type norms
  4. The dual of the space $E\widehat{\otimes}_{\alpha_\lambda'}F$
  5. Tensor characterization for $(\ell_p^{\rm mid})^u(E)$

Key Result

Proposition 2.2

Let $X$ be a sequence class. It follows that:

Theorems & Definitions (35)

  • Definition 1.1
  • Example 1.2
  • Example 1.3
  • Example 2.1
  • Proposition 2.2
  • Example 2.3
  • Definition 2.4
  • Example 2.5
  • Definition 2.6
  • Example 2.7
  • ...and 25 more