Linear extensions associated with abstract functional operators
type: Item
instance of: scholarly article
title: Linear extensions associated with abstract functional operators
zbMATH Open document ID: 1167.47034
author: I. Yu. Trubnikov
author: A. B. Antonevich
publication date: 2009-02-26T00:00:00Z
review text: The authors obtain generalizations of known theorems about the relationship between the invertibility of operators and the hyperbolicity of the associated linear extensions to the case of abstract functional operators. Recall that an abstract functional operator is defined as element of a given C\(^*\)-algebra \(B\) with a structure consisting of a closed C\(^*\)-subalgebra \(A \subset B\) and a unitary element \(T \in B\) such that the mapping \(a \to TaT^{-1}\) is an automorphism of \(A\) and the set of finite sums \(\sum a_kT^k\), \(a_k \in A\), is norm dense in \(B\).
Mathematics Subject Classification ID: 47C15
Mathematics Subject Classification ID: 46L05
zbMATH DE Number: 5519857
zbMATH Keywords: \(C^*\)-algebra
zbMATH Keywords: functional operator
zbMATH Keywords: weighted shift operator
zbMATH Keywords: spectrum of an operator
zbMATH Keywords: linear extension
zbMATH Keywords: hyperbolicity
reviewed by: Cătălin Badea
MaRDI profile type: Publication
full work available at URL: s10688-008-0007-5
OpenAlex ID: W2070694585
cites work: Q4277008
cites work: Q5658860
cites work: The structure of algebras of operator fields
cites work: Q3320942
DOI: 10.1007/S10688-008-0007-5
published in: Functional Analysis and Its Applications
description: scientific article; zbMATH DE number 5519857