On orthogonally additive operators in Köthe-Bochner spaces
type: Item
instance of: scholarly article
title: On orthogonally additive operators in Köthe-Bochner spaces
author: R. Ch. Kulaev
author: Elena K. Basaeva
author: M. Pliev
published in: Results in Mathematics
publication date: 2021-06-23T00:00:00Z
review text: The authors consider the narrowness of orthogonally additive operators in the Köthe-Banach spaces in the sense of [\textit{P.-K. Lin}, Köthe-Bochner function spaces. Boston, MA: Birkhäuser (2004; Zbl 1054.46003)]. They use the technique of domination as presented in [\textit{A. G. Kusraev}, Dominated operators. Transl. from the Russian by the author and edited by S. S. Kutateladze. Dordrecht: Kluwer Academic Publishers (2000; Zbl 0983.47025)] to show that a dominated orthogonally additive operator \(T\) to a Banach lattice with \(o\)-continuous norm is narrow iff so is the exact dominant of \(T\). Some close results are also given.
Mathematics Subject Classification ID: 47H30
Mathematics Subject Classification ID: 46A40
zbMATH DE Number: 7362286
zbMATH Keywords: orthogonally additive operator
zbMATH Keywords: dominated operator
zbMATH Keywords: exact dominant
zbMATH Keywords: \(C\)-compact operator
zbMATH Keywords: narrow operator
zbMATH Keywords: Köthe-Bochner space
zbMATH Keywords: lattice-normed space
zbMATH Keywords: Banach lattice
reviewed by: S. S. Kutateladze
MaRDI profile type: Publication
full work available at URL: s00025-020-01327-9
OpenAlex ID: W3119553416
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DOI: 10.1007/S00025-020-01327-9
description: scientific article; zbMATH DE number 7362286