不可分重排不变空间中的正交性

Pub Date : 2021-01-01 DOI:10.1070/SM9543

S. V. Astashkin, E. Semenov

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引用次数: 0

摘要

设为不可分离重排不变空间，设为中有界函数空间的闭包。正交于的元素，即，对于每个元素，都研究了这样的元素。讨论了在Marcinkiewicz空间或Orlicz空间中正交元素集的特征。如果一个Orlicz空间具有卢森堡范数，则该集合是和的代数和。每一个不可分离的重排不变空间，证明包含该空间的渐近等距副本。参考书目:17篇。

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Orthogonality in nonseparable rearrangement-invariant spaces

Let be a nonseparable rearrangement-invariant space and let be the closure of the space of bounded functions in . Elements of orthogonal to , that is, elements , , such that for each , are investigated. The set of orthogonal elements is characterized in the case when is a Marcinkiewicz or an Orlicz space. If an Orlicz space is considered with the Luxemburg norm, then the set is the algebraic sum of and . Each nonseparable rearrangement-invariant space such that is shown to contain an asymptotically isometric copy of the space . Bibliography: 17 titles.

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