Ideal structure and factorization properties of the regular kernel operators
type: Item
instance of: scholarly article
title: Ideal structure and factorization properties of the regular kernel operators
author: N. E. Zubov
published in: Positivity
publication date: 2021-05-07T00:00:00Z
review text: Let \(X,Y\) be two Banach lattices such that \(X_+,Y_+\) represent their respective positive cones. We say that a linear map \(T:X\to Y\) is positive when the image of \(X_+\) (by \(T\)) is included in \(Y_+\) and \(T\) is regular if it is expressed as a linear combination of positive maps. Let \(\mathcal{L}^r(X,Y)\) be the linear space of all \(Y\)-valued regular maps on \(X\). Let \(E,F\) be Banach lattices and \(L\in \mathcal{L}^r(E,F) \), we say that \(T\in \mathcal{L}^r(X,Y)\) is an \(r\)-factors through \(L\) if there are \((R,S)\in \mathcal{L}^r(F,Y)\times \mathcal{L}^r(X,E)\) such that \(T=RLS\). Let \((\Omega,\Sigma,\mu)\) be a \(\sigma\)-finite measure and \(L_p(\mu)\) be the space of \(p\)-integrable functions w.r.t the measure \(\mu\). The authors state sufficient conditions for an \(r\)-factors through \(L_p(\mu)\) to be an \(r\)-factors through \(l_p\).
reviewed by: Mohammed El Aïdi
Mathematics Subject Classification ID: 47B34
Mathematics Subject Classification ID: 47B60
Mathematics Subject Classification ID: 46B28
Mathematics Subject Classification ID: 47B07
Mathematics Subject Classification ID: 47L10
Mathematics Subject Classification ID: 46B42
Mathematics Subject Classification ID: 47B65
zbMATH DE Number: 7345717
zbMATH Keywords: algebra ideal
zbMATH Keywords: Banach lattice
zbMATH Keywords: kernel operator
zbMATH Keywords: order ideal
zbMATH Keywords: regular operator
MaRDI profile type: Publication
full work available at URL: s11117-019-00728-7
OpenAlex ID: W2996653473
Wikidata QID: Q126587678
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DOI: 10.1007/S11117-019-00728-7
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description: scientific article; zbMATH DE number 7345717