Leibniz Seminorms and Best Approximation from C*-subalgebras
Operator Algebras
2011-12-13 v4 Functional Analysis
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.
Keywords
Cite
@article{arxiv.1008.3733,
title = {Leibniz Seminorms and Best Approximation from C*-subalgebras},
author = {Marc A. Rieffel},
journal= {arXiv preprint arXiv:1008.3733},
year = {2011}
}
Comments
24 pages. Intended for the proceedings of the conference "Operator Algebras and Related Topics". v2: added a corollary to the main theorem, plus several minor improvements v3: much simplified proof of a key lemma, corollary to main theorem added v4: Many minor improvements. Section numbers increased by 1