Banach spaces for which the space of operators has 2 ? closed ideals
Banach spaces for which the space of operators has 2 ? closed ideals
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Banach 空间的算子空间有 2 ？
DOI：
10.1017/fms.2021.23
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发表时间：
2021
期刊：
影响因子：
--
通讯作者：
Zsák, András
中科院分区：
文献类型：
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作者：
Freeman, Daniel;Schlumprecht, Thomas;Zsák, András
我们给出了从Banach空间X到Banach空间Y的算子空间L（，）有2个闭理想的一般条件，其中是连续统的基数。这些结果适用于经典序列空间和Tsirelson型空间。特别地，我们证明了L（L_∞）中闭理想集的基数对所有1<∞都恰为2.
We formulate general conditions which imply that L (,), the space of operators from a Banach space X to a Banach space Y, has 2 closed ideals, where is the cardinality of the continuum. These results are applied to classical sequence spaces and Tsirelson-type spaces. In particular, we prove that the cardinality of the set ofclosed ideals in L (ℓ⊕ ℓ) is exactly 2 for all 1<<<∞.