A Lebesgue-type decomposition on one side for sesquilinear forms

TL;DR

This paper introduces a Lebesgue-type decomposition for sesquilinear forms that are not necessarily positive, focusing on their behavior relative to a positive form on one side, under boundedness conditions.

Contribution

It presents a novel decomposition method for non-positive sesquilinear forms on one side, expanding the theoretical understanding of their structure.

Findings

Decomposition applies to generic forms satisfying boundedness.

Provides a framework for analyzing non-positive sesquilinear forms.

Enhances the theoretical tools for form analysis in functional analysis.

Abstract

Sesquilinear forms which are not necessarily positive may have a different behavior, with respect to a positive form, on each side. For this reason a Lebesgue-type decomposition on one side is provided for generic forms satisfying a boundedness condition.