New s-number classes and summing classes of bilinear operators

IF 1 3区数学 Q1 MATHEMATICS

Annals of Functional Analysis Pub Date : 2025-08-20 DOI:10.1007/s43034-025-00464-y

Eduardo Brandani da Silva, Dicesar Lass Fernandez

引用次数: 0

Abstract

We introduce classes of bilinear operators of \(\ell _{p,q}\)-type, i.e. classes of operators in which their sequences of s-numbers are in \(\ell _{p,q},\) and their properties and relationships are studied. We also introduce two classes of summing bilinear operators: the class \(\Pi _{p,q;r}^{ss}\) of strongly summing operators, and the class \(\Pi _{p,q;r,s}^{as}\) of absolutely summing operators. These classes share some properties with similar proofs. But, some others properties are specific for one or the other class. Also, they are somewhat more general than the multilinear summing classes introduced before by several authors. Relationships between classes of \(\ell _{p,q}\)-type and summing classes are given.

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双线性算子的新s数类和和类

引入了\(\ell _{p,q}\)型双线性算子类，即s-数序列在\(\ell _{p,q},\)中的算子类，并研究了它们的性质和关系。我们还引入了两类求和双线性算子：强求和算子\(\Pi _{p,q;r}^{ss}\)类和绝对求和算子\(\Pi _{p,q;r,s}^{as}\)类。这些类具有一些具有相似证明的属性。但是，其他一些属性是特定于一个或另一个类的。此外，它们比之前由几个作者介绍的多线性求和类更通用。给出了\(\ell _{p,q}\)型类与求和类之间的关系。

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

Annals of Functional Analysis MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.00

自引率

10.00%

发文量

期刊介绍： Annals of Functional Analysis is published by Birkhäuser on behalf of the Tusi Mathematical Research Group. Ann. Funct. Anal. is a peer-reviewed electronic journal publishing papers of high standards with deep results, new ideas, profound impact, and significant implications in all areas of functional analysis and all modern related topics (e.g., operator theory). Ann. Funct. Anal. normally publishes original research papers numbering 18 or fewer pages in the journal’s style. Longer papers may be submitted to the Banach Journal of Mathematical Analysis or Advances in Operator Theory. Ann. Funct. Anal. presents the best paper award yearly. The award in the year n is given to the best paper published in the years n-1 and n-2. The referee committee consists of selected editors of the journal.