oτ-Continuous, Lebesgue, KB, and Levi Operators Between Vector Lattices and Topological Vector Spaces

被引：0

作者：

Alpay, Safak ^{[1
]}

Emelyanov, Eduard ^{[2
]}

Gorokhova, Svetlana ^{[3
]}

机构：

[1] Middle East Tech Univ, Dept Math, TR-06800 Ankara, Turkey

[2] Sobolev Inst Math, Novosibirsk 630090, Russia

[3] Uznyj Matematiceskij Inst VNC RAN, Vladikavkaz 362027, Russia

来源：

RESULTS IN MATHEMATICS | 2022年 / 77卷 / 03期

关键词：

Topological vector space; locally solid lattice; Banach lattice; order convergence; domination property; adjoint operator; BANACH-LATTICES; UO-CONVERGENCE; DUNFORD-PETTIS; COMPACT;

D O I：

10.1007/s00025-022-01650-3

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We investigate o tau-continuous/bounded/compact and Lebesgue operators from vector lattices to topological vector spaces; the Kantorovich-Banach operators between locally solid lattices and topological vector spaces; and the Levi operators from locally solid lattices to vector lattices. The main idea of operator versions of notions related to vector lattices lies in redistributing topological and order properties of a topological vector lattice between the domain and range of an operator under investigation. Domination properties for these classes of operators are studied.

引用

页数：25

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[1] oτ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$o\tau $$\end{document}-Continuous, Lebesgue, KB, and Levi Operators Between Vector Lattices and Topological Vector Spaces
Safak Alpay
Eduard Emelyanov
Svetlana Gorokhova
Results in Mathematics, 2022, 77 (3)
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