算子II的子理想
Subideals of operators II
摘要：
一个子理想（也称为J-理想）是一个理想的B（H）-理想J.本文是续集子理想的运营商在那里一个完整的表征主要然后number-generated J-理想获得了第一次推广1983年的工作方和Radjavi谁确定的主要K（H）-理想也是B（H）-理想。在这里我们确定哪些可数生成的J-理想是B（H）-理想，以及在没有连续统假设的情况下，哪些具有基数小于的生成集的J-理想是B（H）-理想。本文中的这些和一些其它结果是基于相关商空间的维数。我们用它来刻画这些J-理想，并解决有关次理想的其他问题。在我们的研究中，一个关键的性质被证明是J内的B（H）-理想I的J-软性，即IJ = I，这是Kaftal-Weiss最近引入的B（H）-理想软性概念的推广，并且Mityagin和Pietsch早期在巴拿赫空间中利用了这一概念。
英文摘要：
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.
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