Orthogonality in nonseparable rearrangement-invariant spaces

IF 0.8 4区数学 Q2 MATHEMATICS

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

S. V. Astashkin, E. Semenov

引用次数: 0

Abstract

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.

查看原文本刊更多论文

不可分重排不变空间中的正交性

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。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Sbornik Mathematics 数学-数学

CiteScore

1.40

自引率

12.50%

发文量

审稿时长

6-12 weeks

期刊介绍： The Russian original is rigorously refereed in Russia and the translations are carefully scrutinised and edited by the London Mathematical Society. The journal has always maintained the highest scientific level in a wide area of mathematics with special attention to current developments in: Mathematical analysis Ordinary differential equations Partial differential equations Mathematical physics Geometry Algebra Functional analysis