Operator algebra as an application of logarithmic representation of infinitesimal generators

TL;DR

This paper introduces an operator algebra framework using logarithmic representation of infinitesimal generators, characterizing unbounded generators as modules over Banach algebras, advancing the mathematical understanding of operator structures.

Contribution

It presents a novel approach to operator algebra via logarithmic representation, specifically characterizing unbounded infinitesimal generators as modules over Banach algebras.

Findings

Characterization of unbounded infinitesimal generators as modules over Banach algebra

Development of a logarithmic representation framework for operator algebra

Extension of operator algebra theory to include generally-unbounded generators

Abstract

The operator algebra is introduced based on the framework of logarithmic representation of infinitesimal generators. In conclusion a set of generally-unbounded infinitesimal generators is characterized as a module over the Banach algebra.