Remarks on j-$j-$eigenfunctions of operators

被引：1

作者：

Edmunds, David E. ^{[1
]}

Lang, Jan ^{[2
]}

机构：

[1] Univ Sussex, Dept Math, Brighton, England

[2] Ohio State Univ, Dept Math Sci, 100 Math Tower,231 W 18th Ave, Columbus, OH 43210 USA

来源：

MATHEMATISCHE NACHRICHTEN | 2023年 / 296卷 / 03期

关键词：

approximation numbers; compact operators; Gelfand numbers; generalization of Hilbert-Schmidt theorem; Hilbertian map; j-eigenfunctions; p-compactness; P-COMPACT OPERATORS; EIGENVALUES; SPACES;

D O I：

10.1002/mana.202100417

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The paper is largely concerned with the possibility of obtaining a series representation for a compact linear map T acting between Banach spaces. It is known that, using the notions of j-$j-$eigenfunctions and j-$j-$ eigenvalues, such a representation is possible under certain conditions on T. Particular cases discussed include those in which T can be factorized through a Hilbert space, or has certain s-numbers that are fast-decaying. The notion of p-compactness proves to be useful in this context; we give examples of maps that possess this property.

引用

页码：1071 / 1086

页数：16

共 49 条

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