Differential subalgebras and norm-controlled inversion

TL;DR

This paper investigates the properties of differential $*$-subalgebras within symmetric $*$-algebras, focusing on conditions for norm-controlled inversion to understand their algebraic and analytical structure.

Contribution

It introduces new results on norm-controlled inversion specifically for differential $*$-subalgebras of symmetric $*$-algebras, expanding the theoretical framework.

Findings

Established criteria for norm-controlled inversion in differential $*$-subalgebras

Extended the understanding of algebraic structures in symmetric $*$-algebras

Provided new theoretical insights into the inversion process within these subalgebras

Abstract

In this paper, we consider the norm-controlled inversion for differential $*$-subalgebras of a symmetric $*$-algebra with common identity and involution.