On latticially nonatomic subdifferentials
type: Item
instance of: scholarly article
title: On latticially nonatomic subdifferentials
zbMATH Open document ID: 0862.46011
DOI: 10.1007/BF02106620
author: V. A. Radnaev
published in: Siberian Mathematical Journal
publication date: 1997-05-25T00:00:00Z
review text: In [Interuniv. thematic Work Collect., No. 2, Yaroslavl 1978, 132-147 (1978; Zbl 0455.46025)] \textit{G. Ya. Lozanovskij} characterized Banach \(K_\sigma\)-spaces \((E,|\cdot|)\) whose conjugate spaces \(E^*\) are nonatomic. In [Indag. Math., New Ser. 1, No. 3, 391-395 (1990; Zbl 0731.46008)] \textit{B. de Pagter} and \textit{W. Wnuk} extended the Lozanovskij result to the case of Banach lattices. In the present article we study operators that act from a vector lattice into an arbitrary \(K\)-space and establish criteria for latticial nonatomicity of a subdifferential or, in other words, the absence of nonzero lattice homomorphisms in the subdifferential under study. With the help of the criteria, we characterize a Banach-Kantorovich lattice whose conjugate space is latticially nonatomic. The obtained results generalize the criteria of Lozanovskij and de Pagter and Wnuk for nonatomicity of the conjugate of a Banach lattice.
Mathematics Subject Classification ID: 46B42
Mathematics Subject Classification ID: 46B40
Mathematics Subject Classification ID: 47B60
Mathematics Subject Classification ID: 46G05
zbMATH DE Number: 917097
zbMATH Keywords: operators that act from a vector lattice into an arbitrary \(K\)-space
zbMATH Keywords: latticial nonatomicity of a subdifferential
zbMATH Keywords: absence of nonzero lattice homomorphisms
zbMATH Keywords: Banach-Kantorovich lattice
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 917097