Orthogonality in nonseparable rearrangement-invariant spaces
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Published:2021-11-01
Issue:11
Volume:212
Page:1553-1570
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ISSN:1064-5616
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Container-title:Sbornik: Mathematics
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language:
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Short-container-title:Sb. Math.
Author:
Astashkin S. V.,Semenov E. M.
Abstract
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.
Funder
Russian Foundation for Basic Research
Ministry of Science and Higher Education of the Russian Federation
Subject
Algebra and Number Theory