Bishop-Phelps-Bollobás当域为L∞时正算子的性质

IF 1.1 2区数学 Q1 MATHEMATICS Bulletin of Mathematical Sciences Pub Date : 2019-07-19 DOI:10.1142/S166436072050023X

M. Acosta, M. Soleimani-Mourchehkhorti

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引用次数: 2

摘要

证明了从[公式:见文]到[公式:见文]的正算子类对于任何正测度[公式:见文]，只要[公式:见文]是具有弱单位的一致单调巴拿赫格，都具有Bishop-Phelps-Bollobás性质。同样的结果也适用于任何一致单调的Banach格对[公式:见文][公式:见文]进一步我们证明了这些结果在[公式:见文]是严格单调的情况下是最优的。

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Bishop-Phelps-Bollobás property for positive operators when the domain is L∞

We prove that the class of positive operators from [Formula: see text] to [Formula: see text] has the Bishop-Phelps-Bollobás property for any positive measure [Formula: see text], whenever [Formula: see text] is a uniformly monotone Banach lattice with a weak unit. The same result also holds for the pair [Formula: see text] for any uniformly monotone Banach lattice [Formula: see text] Further we show that these results are optimal in case that [Formula: see text] is strictly monotone.

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来源期刊

Bulletin of Mathematical Sciences MATHEMATICS-

CiteScore

2.10

自引率

0.00%

发文量

审稿时长

13 weeks

期刊介绍： The Bulletin of Mathematical Sciences, a peer-reviewed, open access journal, will publish original research work of highest quality and of broad interest in all branches of mathematical sciences. The Bulletin will publish well-written expository articles (40-50 pages) of exceptional value giving the latest state of the art on a specific topic, and short articles (up to 15 pages) containing significant results of wider interest. Most of the expository articles will be invited. The Bulletin of Mathematical Sciences is launched by King Abdulaziz University, Jeddah, Saudi Arabia.

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