Lebesgue Spaces and Inclusion Relation

TL;DR

This paper discusses inclusion relations among Lebesgue spaces, applying Villani's closed graph theorem technique, and explores automatic continuity of multiplicative linear functionals on Banach algebras.

Contribution

It extends Villani's methods to additional spaces and establishes new inclusion relations and automatic continuity results.

Findings

Derived new inclusion relations among Lebesgue and related spaces

Applied closed graph theorem technique to prove inclusion results

Established automatic continuity of multiplicative linear functionals

Abstract

The proofs of A. Villani on inclusion relations among classical Lebesgue spaces are dicussed. The techinque of using closed graph theorem, due to Villani, is applied to derive results on inclusion relations among some more additional spaces. An application of automatic continuity of multiplicative linear functionals on Banach algebras is found.