Approximate Double Commutants and Distance Formulas
Operator Algebras
2012-10-22 v1 Functional Analysis
Abstract
We extend work of the first author concering relative double commutants and approximate double commutants of unital subalgebras of unital C*-algebras, including metric versions involving distance estimates. We prove metric results for AH subalgebras of von Neumann algebras or AF subalgebras of primitive C*-algebras. We prove other general results, including some for nonselfadjoint commutative subalgebras, using C*-algebraic versions of the Stone-Weierstrass and Bishop-Stone-Weierstrass theorems.
Cite
@article{arxiv.1210.5285,
title = {Approximate Double Commutants and Distance Formulas},
author = {Don Hadwin and Junhao Shen},
journal= {arXiv preprint arXiv:1210.5285},
year = {2012}
}