Compactness in Lorentz sequence spaces

TL;DR

This paper explores the concept of compactness in Lorentz sequence spaces, providing definitions, norm calculations, and criteria for compactness using seminorms to enhance understanding and analysis.

Contribution

It introduces practical compactness criteria for Lorentz sequence spaces based on seminorms, advancing the theoretical framework and analytical tools for these spaces.

Findings

Developed methods to define Lorentz sequence spaces

Provided criteria for compactness in these spaces

Utilized seminorms to establish compactness conditions

Abstract

In this paper we are going to discuss compactness in Lorentz sequence spaces. Firstly, it will be shown how to define such a space, check whether a sequence belongs to it and calculate its norm. Equipped with this knowledge, we will proceed to propose usable compactness criteria for Lorentz sequence spaces, employing the concept of seminorms.