Subideals of Operators II |
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Authors: | Sasmita Patnaik Gary Weiss |
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Institution: | 1. Department of Mathematics, University of Cincinnati, Cincinnati, OH, 45221-0025, USA
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Abstract: | 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?CWeiss and earlier exploited for Banach spaces by Mityagin and Pietsch. |
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