2012/09/27 by S. Patnaik, Sasmita Patnaik, Patnaik, S. +3
Mathematics · #13C05 #13C12 #47B07 #47B10 #47B37 #Advanced Banach Space Theory #Advanced Topology and Set Theory #Approximation Theory and Sequence Spaces #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA) #Primary: 47L20 #Secondary: 47B47 #math.FA #math.OA #msc:13C05 #msc:13C12 #msc:47B07 #msc:47B10 #msc:47B37 #msc:47B47 #msc:47L20
paper · pdf · doi:10.48550/arxiv.1209.6323
9 pages, J. Integral Equations and Operator Theory, to appear
arxiv created 2012/09/27 · openalex publication_date 2012/09/27 · arxiv updated 2012/09/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A subideal (also called a J-ideal) is an ideal of a B(H)-ideal J. This paper is the sequel to Subideals of operators where a complete characterization of principal and then finitely generated J-ideals were obtained by first generalizing the 1983 work of Fong and Radjavi who determined which principal K(H)-ideals are also B(H)-ideals. Here we determine which countably generated J-ideals are B(H)-ideals, and in the absence of the continuum hypothesis which J-ideals with generating sets of cardinality less than the continuum are B(H)-ideals. These and some other results herein are based on the dimension of a related quotient space. We use this to characterize these J-ideals and settle additional questions about subideals. A key property in our investigation turned out to be J-softness of a B(H)-ideal I inside J, that is, IJ = I, a generalization of a recent notion of softness of B(H)-ideals introduced by Kaftal-Weiss and earlier exploited for Banach spaces by Mityagin and Pietsch.