Leibniz Seminorms and Best Approximation from C*-subalgebras

TL;DR

This paper investigates the properties of Leibniz seminorms derived from C*-subalgebras and explores best approximation techniques within unital C*-algebras, revealing new structural insights.

Contribution

It demonstrates that a specific pull-back seminorm is strongly Leibniz and examines approximation methods in unital C*-algebras, advancing understanding of their algebraic structure.

Findings

Pull-back seminorm L is strongly Leibniz under given conditions

Characterization of best approximation in unital C*-algebras

Insights into the structure of C*-subalgebras and approximation

Abstract

We show that if B is a C*-subalgebra of a C*-algebra A such that B contains a bounded approximate identity for A, and if L is the pull-back to A of the quotient norm on A/B, then L is strongly Leibniz. In connection with this situation we study certain aspects of best approximation of elements of a unital C*-algebra by elements of a unital C*-subalgebra.