Local characterisation of approximately finite operator algebras

2000/11/20 by P. A. Haworth, Haworth, P. A.
Mathematics · #47A55 #47L40 #FOS: Mathematics #Operator Algebras (math.OA) #math.OA #msc:47A55 #msc:47L40

paper · pdf · doi:10.48550/arxiv.math/0011143

20 pages

arxiv created 2000/11/20 · arxiv updated 2009/11/30

Abstract

We show that the family of nest algebras with r non-zero nest projections is stable, in the sense that an approximate containment of one such algebra within another is close to an exact containment. We use this result to give a local characterisation of limits formed from this family. We then consider quite general regular limit algebras and characterise these algebras using a local condition which reflects the assumed regularity of the system.

Related

• Compact Operators and Nest Representations of Limit Algebras
• Stable normed algebras
• Limits of Finite Dimensional Nest Algebras
• Minimal boundaries for operator algebras
• Applications of operator space theory to nest algebra bimodules