Measurable bundles of Banach lattices
type: Item
instance of: scholarly article
title: Measurable bundles of Banach lattices
zbMATH Open document ID: 1217.46012
published in: Positivity
publication date: 2011-01-17T00:00:00Z
review text: The theory of Banach bundles has proved to have many applications in analysis. For example, continuous and measurable Banach bundles are used for representing various objects in functional analysis. A Banach-Kantorovich space over a Dedekind complete vector lattice is linearly isometric to the space of almost global sections of a suitable continuous Banach bundle over an extremally disconnected compactum. The uniqueness class for this representation was established by \textit{A. E. Gutman} in [Sib. Adv. Math. 3, No.~3, 1--55 (1993; Zbl 0854.46004)]. The next milestone was to specify this representation result if the norming lattice is an ideal function space. In this case, the representing object is a measurable Banach bundle and the uniqueness class is comprised of liftable Banach bundles. This is also due to A. E. Gutman. The objective of the present paper is to outline a portion of Gutman's theory of liftable Banach bundles of Banach lattices and to give applications to the representation of dominable operators.
Mathematics Subject Classification ID: 46B42
Mathematics Subject Classification ID: 46M20
Mathematics Subject Classification ID: 46G15
Mathematics Subject Classification ID: 47B60
Mathematics Subject Classification ID: 47A60
zbMATH DE Number: 5837808
zbMATH Keywords: Banach lattice
zbMATH Keywords: measurable Banach bundle
zbMATH Keywords: measurable section
zbMATH Keywords: lifting
zbMATH Keywords: dual bundle
zbMATH Keywords: dominated operator
zbMATH Keywords: functional calculus
author: Anatoly G. Kusraev
reviewed by: Şafak Alpay
MaRDI profile type: Publication
full work available at URL: s11117-010-0063-y
OpenAlex ID: W2087097605
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DOI: 10.1007/S11117-010-0063-Y
description: scientific article; zbMATH DE number 5837808