Remarks on normal operators on Banach spaces
type: Item
instance of: scholarly article
title: Remarks on normal operators on Banach spaces
zbMATH Open document ID: 0635.47015
DOI: 10.1007/BF02843901
author: Erich Marschall
publication date: 1986-01-01T00:00:00Z
review text: A closed densely defined operator T on a Banach space X is called normal, iff \(T\in [C^ 0({\hat {\mathbb{C}}})]\), i.e. there is a homomorphism (functional calculus) \(f\to f(T)\) of the continuous functions on \({\hat {\mathbb{C}}}:={\mathbb{C}}\cup \{\infty \}\) into the bounded linear operators with \(\| f(T)\| \leq \sup \{| f(z)|:z\in {\hat {\mathbb{C}}}\}\) and which extends the analytic calculus. It is shown that this definition agrees with that of \textit{T. W. Palmer} [Trans. Amer. Math. Soc. 133, 385- 414 (1968; Zbl 0169.169)]. The functional calculus yields simple proofs of properties which are well-known for normal operators on Hilbert spaces. In the second part the methods are applied to semi-groups of normal operators resp. cosine operator functions.
Mathematics Subject Classification ID: 47A60
Mathematics Subject Classification ID: 47D03
Mathematics Subject Classification ID: 47D99
Mathematics Subject Classification ID: 47B15
zbMATH DE Number: 4034451
zbMATH Keywords: normal operators on Banach spaces
zbMATH Keywords: closed densely defined operator
zbMATH Keywords: functional calculus
zbMATH Keywords: semi-groups of normal operators
zbMATH Keywords: cosine operator functions
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02843901
OpenAlex ID: W2084665925
published in: Rendiconti del Circolo Matematico di Palermo
description: scientific article; zbMATH DE number 4034451