A note on two-sided ideals in locally C*-algebras

TL;DR

This paper proves a property of two-sided ideals in locally C*-algebras, showing the positive part of their sum equals the sum of their positive parts, enhancing understanding of their structure.

Contribution

It establishes a new equality relating positive parts of sums of ideals in locally C*-algebras, contributing to the structural theory of these algebras.

Findings

Positive part of (I+J) equals sum of positive parts of I and J

Clarifies structure of two-sided ideals in locally C*-algebras

Enhances understanding of ideal operations in non-commutative topology

Abstract

In the present note we show that if A is a locally C*-algebra, and I and J are closed two-sided ideals in A, then the positive part of (I+J) is equal to the sum of positive parts of I and J.