Spectrum and functions of operators on direct families of Banach spaces
type: Item
instance of: scholarly article
title: Spectrum and functions of operators on direct families of Banach spaces
zbMATH Open document ID: 1256.47004
published in: Methods and Applications of Analysis
publication date: 2011-01-13T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.maa/1286890994
review text: Direct families of Banach spaces, which generalise the notion of direct integrals of Hilbert spaces and the notion of Banach spaces with mixed norms, are considered in this paper. The spectrum, resolvent and analytic functions of bounded linear operators on such direct families of Banach spaces are investigated, and applications to partial integral operators are given. The paper ends with an application to an integrodifferential equation of Barbashin type.
Mathematics Subject Classification ID: 47A10
Mathematics Subject Classification ID: 46E15
Mathematics Subject Classification ID: 47A56
Mathematics Subject Classification ID: 47G10
Mathematics Subject Classification ID: 45P05
zbMATH DE Number: 5835908
zbMATH Keywords: direct families of Banach spaces
zbMATH Keywords: spectrum
zbMATH Keywords: mixed norms
zbMATH Keywords: partial integral operator
zbMATH Keywords: Barbashin type equation
zbMATH Keywords: linear operator
zbMATH Keywords: resolvent
zbMATH Keywords: perturbation
author: Michael I. Gil'
reviewed by: Cătălin Badea
MaRDI profile type: Publication
DOI: 10.4310/MAA.2009.V16.N4.A7
description: scientific article; zbMATH DE number 5835908