Duality and o − O-structure in non reflexive Banach spaces

IF 0.6 Q3 MULTIDISCIPLINARY SCIENCES

Atti Accademia Peloritana dei Pericolanti-Classe di Scienze Fisiche Matematiche e Naturali Pub Date : 2020-12-13 DOI:10.1478/AAPP.98S2A7

Luigi d’Onofrio, C. Sbordone, Roberta Schiattarella

引用次数: 0

Abstract

Let E be a Banach space with a supremum type norm induced by a collection of functionals ℒ ⊂ X * where X is a reflexive Banach space. Familiar spaces of this type are BMO , BV , C 0,α (0 1. For most of these spaces E , the predual E * exists and can be defined by atomic decomposition of its elements. Another typical result, when it is possible to define a rich vanishing subspace E 0 ⊂ E is the "two star theorem", namely ( E 0 )*= E * . This fails for E = BV and E = C 0,1 = Lip .

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非自反Banach空间中的对偶性和o−o结构

设E是Banach空间，具有由泛函集合诱导的上确界型范数ℒ ⊂ 其中X是自反Banach空间。这种类型的常见空间是BMO，BV，C0，α（01。对于这些空间E中的大多数空间，存在先验E*，并且可以通过其元素的原子分解来定义。另一个典型的结果，当可以定义一个丰富的消失子空间E 0⊂E时，是“双星定理”，即（E 0）*=E*。E=BV和E=C 0,1=唇缘时，此操作失败。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Atti Accademia Peloritana dei Pericolanti-Classe di Scienze Fisiche Matematiche e Naturali MULTIDISCIPLINARY SCIENCES-

CiteScore

3.80

自引率

0.00%

发文量

审稿时长

31 weeks

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