Lambert Multipliers Between $L^P$-spaces as a Banach Algebra

TL;DR

This paper introduces a new norm for Lambert multipliers on L^p-spaces, proving they form a commutative Banach algebra, and characterizes Fredholm *-multiplication operators on these spaces.

Contribution

It establishes that Lambert multipliers form a commutative Banach algebra under a new norm and characterizes Fredholm *-multiplication operators on L^p-spaces.

Findings

K^*_p is a Banach algebra under the new norm

Lambert multipliers are characterized as a commutative Banach algebra

Fredholm *-multiplication operators are explicitly characterized

Abstract

For 1 ≤ p < ∞, it is known that the set K^*_p contains of all Lambert multipliers acting between L^p-spaces is a Banach space. In this study, we introduce a new induced norm by conditional expectation operators to show that K^*_p is a commutative Banach algebra with respect to this norm. Furthermore, in main result, the Fredholm *-multiplication operators on L^p-spaces are characterized, and some more results are obtained.