Algebras of log-integrable functions and operators

TL;DR

This paper demonstrates that specific spaces of log-integrable functions and operators form complete topological *-algebras and investigates their relationship with the Nevanlinna class of holomorphic functions.

Contribution

It establishes the topological algebraic structure of log-integrable function and operator spaces and links them to the Nevanlinna class, advancing understanding of their mathematical properties.

Findings

Spaces are complete topological *-algebras

Connections with the Nevanlinna class are explored

Provides a framework for analyzing log-integrable functions and operators

Abstract

We show that certain spaces of log-integrable functions and operators are complete topological *-algebras with respect to a natural metric space structure. We explore connections with the Nevanlinna class of holomorphic functions.