紧双线性算子的插值

IF 1.1 2区数学 Q1 MATHEMATICS

Bulletin of Mathematical Sciences Pub Date : 2019-04-13 DOI:10.1142/s1664360720500022

M. Mastyło, E. B. Silva

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引用次数: 5

摘要

研究了作用于插值巴拿赫空间积上的双线性算子紧性的稳定性。在Aronszajn和Gagliardo意义下，证明了由抽象插值方法生成的Banach空间积上双线性算子的单侧紧性结果。为了得到这些结果，我们证明了双线性算子在满足额外近似性质的对上的紧性的一个关键的单侧双线性插值定理。我们给出了一般情况下的应用，包括皮特方法和一般实插值方法。

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Interpolation of compact bilinear operators

This paper is devoted to the study of the stability of the compactness property of bilinear operators acting on the products of interpolated Banach spaces. We prove one-sided compactness results for bilinear operators on products of Banach spaces generated by abstract methods of interpolation, in the sense of Aronszajn and Gagliardo. To get these results, we prove a key one-sided bilinear interpolation theorem on compactness for bilinear operators on couples satisfying an extra approximation property. We give applications to general cases, including Peetre’s method and the general real interpolation methods.

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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.