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An Application of Kadets-Pełczyński Sets to Narrow Operators

An Application of Kadets-Pełczyński Sets to Narrow Operators

A known analogue of the Pitt compactness theorem for function spaces asserts that if 1 ≤ p < 2 and p < r < ∞, then every operator T : Lp → Lr is narrow. Using a technique developed by M.I. Kadets and A. Pełczyński, we prove a similar result. More precisely, if 1 ≤ p ≤ 2 and F is a Köthe {Ba...

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Main Authors: Krasikova, I.V., Popov, M.M.
Format: Article
Language:English
Published: Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України 2013
Series:Журнал математической физики, анализа, геометрии
Online Access:http://dspace.nbuv.gov.ua/handle/123456789/106739
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spelling irk-123456789-1067392016-10-04T03:02:39Z An Application of Kadets-Pełczyński Sets to Narrow Operators Krasikova, I.V. Popov, M.M. A known analogue of the Pitt compactness theorem for function spaces asserts that if 1 ≤ p < 2 and p < r < ∞, then every operator T : Lp → Lr is narrow. Using a technique developed by M.I. Kadets and A. Pełczyński, we prove a similar result. More precisely, if 1 ≤ p ≤ 2 and F is a Köthe {Banach space on [0; 1] with an absolutely continuous norm containing no isomorph of Lp such that F is subset of Lp, then every regular operator T : Lp → F is narrow. Известный аналог теоремы Питта о компактности для функциональных пространств утверждает, что если 1 ≤ p < 2 и p < r < ∞, то каждый оператор Lp → Lr узкий. Используя технику, разработанную М.И. Кадецем и А. Пелчинским, мы доказываем похожий результат. Именно, если 1 ≤ p ≤ 2 и F - банахово пространство Кете на [0; 1] с абсолютно непрерывной нормой, не содержащее подпространств, изоморфных Lp, причем F является подмножеством Lp, то каждый регулярный оператор T : Lp → F узкий. 2013 Article An Application of Kadets-Pełczyński Sets to Narrow Operators / I.V. Krasikova, M.M. Popov // Журнал математической физики, анализа, геометрии. — 2013. — Т. 9, № 1. — С. 102-107. — Бібліогр.: 14 назв. — англ. 1812-9471 http://dspace.nbuv.gov.ua/handle/123456789/106739 en Журнал математической физики, анализа, геометрии Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
language English
description A known analogue of the Pitt compactness theorem for function spaces asserts that if 1 ≤ p < 2 and p < r < ∞, then every operator T : Lp → Lr is narrow. Using a technique developed by M.I. Kadets and A. Pełczyński, we prove a similar result. More precisely, if 1 ≤ p ≤ 2 and F is a Köthe {Banach space on [0; 1] with an absolutely continuous norm containing no isomorph of Lp such that F is subset of Lp, then every regular operator T : Lp → F is narrow.
format Article
author Krasikova, I.V.
Popov, M.M.
spellingShingle Krasikova, I.V.
Popov, M.M.
An Application of Kadets-Pełczyński Sets to Narrow Operators
Журнал математической физики, анализа, геометрии
author_facet Krasikova, I.V.
Popov, M.M.
author_sort Krasikova, I.V.
title An Application of Kadets-Pełczyński Sets to Narrow Operators
title_short An Application of Kadets-Pełczyński Sets to Narrow Operators
title_full An Application of Kadets-Pełczyński Sets to Narrow Operators
title_fullStr An Application of Kadets-Pełczyński Sets to Narrow Operators
title_full_unstemmed An Application of Kadets-Pełczyński Sets to Narrow Operators
title_sort application of kadets-pełczyński sets to narrow operators
publisher Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
publishDate 2013
url http://dspace.nbuv.gov.ua/handle/123456789/106739
citation_txt An Application of Kadets-Pełczyński Sets to Narrow Operators / I.V. Krasikova, M.M. Popov // Журнал математической физики, анализа, геометрии. — 2013. — Т. 9, № 1. — С. 102-107. — Бібліогр.: 14 назв. — англ.
series Журнал математической физики, анализа, геометрии
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first_indexed 2023-10-18T20:13:36Z
last_indexed 2023-10-18T20:13:36Z
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