Banach空间弱p紧算子的理想及其逼近性质

IF 0.9 4区数学 Q2 Mathematics

Annales Academiae Scientiarum Fennicae-Mathematica Pub Date : 2020-06-01 DOI:10.5186/aasfm.2020.4547

Ju Myung Kim

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引用次数: 4

摘要

研究了弱p紧算子的理想Wp及其逼近性质(Wp- ap)。证明了Wp =Wp◦Wp和Vp = Kup◦W−1 p，且对于1 < p≤∞，当且仅当X上的恒等映射被弱p紧集合上一致收敛拓扑上X上的有限秩算子逼近时，Banach空间X具有Wp- ap。此外，我们还研究了经典序列空间和对偶空间的Wp-AP。

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The ideal of weakly p-compact operators and its approximation property for Banach spaces

We investigate the ideal Wp of weakly p-compact operators and its approximation property (Wp-AP). We prove that Wp =Wp ◦Wp and Vp = Kup ◦W −1 p and that for 1 < p ≤ ∞, a Banach space X has the Wp-AP if and only if the identity map on X is approximated by finite rank operators on X in the topology of uniform convergence on weakly p-compact sets. Also, we study the Wp-AP for classical sequence spaces and dual spaces.

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来源期刊

Annales Academiae Scientiarum Fennicae-Mathematica 数学-数学

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Annales Academiæ Scientiarum Fennicæ Mathematica is published by Academia Scientiarum Fennica since 1941. It was founded and edited, until 1974, by P.J. Myrberg. Its editor is Olli Martio. AASF publishes refereed papers in all fields of mathematics with emphasis on analysis.