Dual of Köthe-Bochner spaces and Radon-Nikodým property
type: Item
instance of: scholarly article
title: Dual of Köthe-Bochner spaces and Radon-Nikodým property
zbMATH Open document ID: 1479.46030
author: Răzvan-Cornel Sfetcu
author: Oana Cojocaru
author: Ion Chiţescu
published in: Rocky Mountain Journal of Mathematics
publication date: 2021-09-10T00:00:00Z
review text: Let \(\rho\) be a saturated function norm on a \(\sigma\)-finite measure space. Suppose that both \(\rho\) and its associated function norm \(\rho'\) are of absolutely continuous type. Let \(X\) be a Banach space such that its dual~\(X'\) has the Radon-Nikodým property. Under the previous assumptions, the main result of the paper under review states that the dual of the Köthe-Bochner space \(L_\rho(X)\) coincides with \(L_{\rho'}(X')\). There are general results on the representation of the dual of a Köthe-Bochner space in the absence of the Radon-Nikodým property, based on lifting theory. See, e.g., Theorem 3.2.4 in [\textit{P.-K. Lin}, Köthe-Bochner function spaces. Boston, MA: Birkhäuser (2004; Zbl 1054.46003)].
Mathematics Subject Classification ID: 46E30
Mathematics Subject Classification ID: 46G10
zbMATH DE Number: 7393755
zbMATH Keywords: Köthe-Bochner space
zbMATH Keywords: Radon-Nikodým property
reviewed by: J. Rodríguez
MaRDI profile type: Publication
full work available at URL: rmj.2021.51.109
OpenAlex ID: W3167759799
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DOI: 10.1216/RMJ.2021.51.109
description: scientific article; zbMATH DE number 7393755