Normal operators and multipliers on complex Banach spaces and a symmetry property of \(L^ 1\)-predual spaces
type: Item
instance of: scholarly article
title: Normal operators and multipliers on complex Banach spaces and a symmetry property of \(L^ 1\)-predual spaces
zbMATH Open document ID: 0544.47018
DOI: 10.1007/BF02760559
author: Ehrhard Behrends
published in: Israel Journal of Mathematics
publication date: 1984-01-01T00:00:00Z
review text: An operator T on a complex Banach space X is called normal if there exists an operator S such that \(({1\over2})(T+S)\) and \(({1\over2}i)(T-S)\) are Hermitian and \(TS=ST.\) We show how \(T:X\to X\) is normal if and only if \(T':X'\to X'\) is normal. Using a generalization of the principle of local reflexivity this result enables us to prove that multipliers on complex \(L^ 1\)-predual spaces are always normal.
Mathematics Subject Classification ID: 47B15
zbMATH DE Number: 3866008
zbMATH Keywords: normal operators on Banach space
zbMATH Keywords: principle of local reflexivity
zbMATH Keywords: multipliers on complex \(L^ 1\)-predual spaces are always normal
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3866008