Nuclear operators on Banach function spaces
type: Item
instance of: scholarly article
title: Nuclear operators on Banach function spaces
zbMATH Open document ID: 1494.47058
author: Marian Nowak
published in: Positivity
publication date: 2021-08-16T00:00:00Z
review text: The author investigates nuclear operators on Banach function spaces. Among other interesting results, it is proved that every nuclear operator \(T:E\longrightarrow X\) between the locally convex space \((E,\tau(E,E^{\prime }))\) and a Banach space \(X\) is Bochner representable, where \(E\) is an order ideal of \(L^{0}\) such that \(L^{\infty }\subset E\subset L^{1}\), with a Riesz norm \(\left\Vert \cdot \right\Vert _{E}\). Especially, if \( E=L^{\infty }\), then the operator \(T\) is nuclear if and only if its representing measure has the Radon-Nikodym property and admits a factorization through some Orlicz space.
reviewed by: Elhadj Dahia
Mathematics Subject Classification ID: 47B38
Mathematics Subject Classification ID: 47B10
Mathematics Subject Classification ID: 46E30
zbMATH DE Number: 7382072
zbMATH Keywords: Banach function spaces
zbMATH Keywords: Mackey topologies
zbMATH Keywords: mixed topologies
zbMATH Keywords: vector measures
zbMATH Keywords: nuclear operators
zbMATH Keywords: Bochner representable operators
zbMATH Keywords: kernel operators
zbMATH Keywords: Radon-Nikodym property
zbMATH Keywords: Orlicz spaces
zbMATH Keywords: Orlicz-Bochner spaces
MaRDI profile type: Publication
full work available at URL: s11117-020-00787-1
OpenAlex ID: W3092383293
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DOI: 10.1007/S11117-020-00787-1
description: scientific article; zbMATH DE number 7382072