Inclusion theorems for grand Lorentz spaces

TL;DR

This paper explores inclusion theorems for grand Lorentz spaces and investigates the convergence of approximate identities within these spaces, contributing to the understanding of their structure and functional properties.

Contribution

It introduces new inclusion theorems for grand Lorentz spaces and analyzes the convergence behavior of approximate identities in these spaces.

Findings

Established inclusion relations between different grand Lorentz spaces.

Proved convergence of approximate identities in these spaces under certain conditions.

Enhanced understanding of the structure and functional analysis of grand Lorentz spaces.

Abstract

In this paper, we consider some inclusion theorems for grand Lorentz spaces $L^{p,q)}\left( X,\mu \right) $ and $\Lambda _{p),\omega }$ where $\mu $ is a finite measure on $\left( X,\Sigma \right) .$ Moreover, we consider the problem of the convergence of approximate identities in these spaces.