On Levi Operators Between Normed and Vector Lattices Full article
| Journal |
Siberian Mathematical Journal
ISSN: 0037-4466 , E-ISSN: 1573-9260 |
||
|---|---|---|---|
| Output data | Year: 2025, Volume: 66, Number: 5, Pages: 1270–1275 Pages count : 6 DOI: 10.1134/S0037446625050167 | ||
| Tags | normed lattice, Levi operator, finite-rank operator, compact operator, KB-space | ||
| Authors |
|
||
| Affiliations |
|
Funding (1)
| 1 | Sobolev Institute of Mathematics | FWNF-2022-0004 |
Abstract:
The notion of a Levi operator is an operator abstraction of the Levi property of a norm or, more generally, of the Levi topology on a locally solid vector lattice. Various aspects of Levi operators have been studied recently by several authors. The present paper is devoted to Levi operators from a normed lattice to a vector lattice. It is proved that every continuous finite-rank operator is a Levi operator. An example is given showing that the sum of a positive rank one operator and a positive compact Levi operator need not be a Levi operator. We prove that every quasi Levi operator is continuous. It is shown that the set of Levi operators on the space of convergent sequences is not complete in the operator norm. Several results concerning the domination problem for Levi operators and the relations between Levi operators and KB-spaces are established.
Cite:
Emelyanov E.Y.
On Levi Operators Between Normed and Vector Lattices
Siberian Mathematical Journal. 2025. V.66. N5. P.1270–1275. DOI: 10.1134/S0037446625050167 WOS Scopus РИНЦ OpenAlex
On Levi Operators Between Normed and Vector Lattices
Siberian Mathematical Journal. 2025. V.66. N5. P.1270–1275. DOI: 10.1134/S0037446625050167 WOS Scopus РИНЦ OpenAlex
Dates:
| Submitted: | Jun 22, 2025 |
| Accepted: | Jul 7, 2025 |
| Published print: | Sep 30, 2025 |
| Published online: | Sep 30, 2025 |
Identifiers:
| Web of science: | WOS:001585885200001 |
| Scopus: | 2-s2.0-105017401273 |
| Elibrary: | 82944339 |
| OpenAlex: | W4414652264 |
Citing:
Пока нет цитирований