On collectively \(L\)-weakly compact sets of operators

IF 0.5 3区数学 Q3 MATHEMATICS

Analysis Mathematica Pub Date : 2025-06-12 DOI:10.1007/s10476-025-00088-3

E. Emelyanov

引用次数: 0

Abstract

A set of bounded linear operators from a Banach space to a Banach lattice is collectively \(L\)-weakly compact whenever union of images of the unit ball is \(L\)-weakly compact. In the present note the Meyer-Nieberg duality theorem is extended to collectively \(L\)-weakly compact sets of operators, the relationship between collectively \(L\)-weakly compact sets and collectively almost limited sets is investigated, and the domination problem for collectively compact and collectively \(L\)-weakly compact sets is studied.

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在集合\(L\) -弱紧算子集上

当单位球的像的并集为\(L\)弱紧时，从Banach空间到Banach格的一组有界线性算子集体为\(L\) -弱紧。本文将Meyer-Nieberg对偶定理推广到算子的集体\(L\) -弱紧集，研究了集体\(L\) -弱紧集与集体几乎有限集的关系，并研究了集体紧集与集体\(L\) -弱紧集的支配问题。

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

Analysis Mathematica MATHEMATICS-

CiteScore

1.00

自引率

14.30%

发文量

审稿时长

>12 weeks

期刊介绍： Traditionally the emphasis of Analysis Mathematica is classical analysis, including real functions (MSC 2010: 26xx), measure and integration (28xx), functions of a complex variable (30xx), special functions (33xx), sequences, series, summability (40xx), approximations and expansions (41xx). The scope also includes potential theory (31xx), several complex variables and analytic spaces (32xx), harmonic analysis on Euclidean spaces (42xx), abstract harmonic analysis (43xx). The journal willingly considers papers in difference and functional equations (39xx), functional analysis (46xx), operator theory (47xx), analysis on topological groups and metric spaces, matrix analysis, discrete versions of topics in analysis, convex and geometric analysis and the interplay between geometry and analysis.