On compact KB operators in Banach lattices On compact KB operators in Banach lattices

We study norm completeness and the domination problem for KB operators, and show that compact KB operators are not necessarily stable under rank one perturbations. It is proved that an order continuous Banach lattice is a KB-space if and only if every positive compact operator on it is KB. Condition...

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Bibliographic Details
Published in:Positivity : an international journal devoted to the theory and applications of positivity in analysis Vol. 29; no. 1; p. 15
Main Author: Emelyanov, Eduard
Format: Journal Article
Language:English
Published: Cham Springer International Publishing 01.02.2025
Springer Nature B.V
Subjects:
Calculus of Variations and Optimal Control; Optimization
Econometrics
Fourier Analysis
Linear operators
Mathematics
Mathematics and Statistics
Operator Theory
Operators (mathematics)
Potential Theory
Compact operator
46B42
47L05
KB operator
Banach lattice
46A40
ISSN:1385-1292, 1572-9281
Online Access:Get full text
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Summary:We study norm completeness and the domination problem for KB operators, and show that compact KB operators are not necessarily stable under rank one perturbations. It is proved that an order continuous Banach lattice is a KB-space if and only if every positive compact operator on it is KB. Conditions on quasi-KB operators to be KB are given.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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ISSN:1385-1292
1572-9281
DOI:10.1007/s11117-024-01109-5