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
收藏
页码：1071 / 1086
页数：16
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