论向量值小李普希茨函数的巴拿赫空间的第二对偶空间

IF 0.6 4区数学 Q3 MATHEMATICS

Kyushu Journal of Mathematics Pub Date : 2020-09-21 DOI:10.2206/kyushujm.75.235

Shinnosuke Izumi

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引用次数: 1

摘要

设\(X\)是紧度量空间\(E\)是巴拿赫空间。\(\lip (X, E)\)表示\(X\)上所有\(E\)值小Lipschitz函数的Banach空间。在若干条件下，我们证明\(\lip (X, E)^{**}\)与\(E^{**}\) -值Lipschitz函数\(\Lip(X, E^{**})\)的Banach空间是等距同构的。此外，我们描述了从\(\lip (X, E)^{**}\)到\(\Lip (X, E^{**})\)的等距同构。

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ON THE SECOND DUAL SPACE OF THE BANACH SPACE OF VECTOR-VALUED LITTLE LIPSCHITZ FUNCTIONS

Let \(X\) be a compact metric space and \(E\) be a Banach space. \(\lip (X, E)\) denotes the Banach space of all \(E\)-valued little Lipschitz functions on \(X\). We show that \(\lip (X, E)^{**}\) is isometrically isomorphic to Banach space of \(E^{**}\)-valued Lipschitz functions \(\Lip(X, E^{**})\) under several conditions. Moreover, we describe the isometric isomorphism from \(\lip (X, E)^{**}\) to \(\Lip (X, E^{**})\).

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来源期刊

Kyushu Journal of Mathematics 数学-数学

CiteScore

0.80

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： The Kyushu Journal of Mathematics is an academic journal in mathematics, published by the Faculty of Mathematics at Kyushu University since 1941. It publishes selected research papers in pure and applied mathematics. One volume, published each year, consists of two issues, approximately 20 articles and 400 pages in total. More than 500 copies of the journal are distributed through exchange contracts between mathematical journals, and available at many universities, institutes and libraries around the world. The on-line version of the journal is published at "Jstage" (an aggregator for e-journals), where all the articles published by the journal since 1995 are accessible freely through the Internet.