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 Funktsional. Anal. i Prilozhen.: Year: Volume: Issue: Page: Find

 Funktsional. Anal. i Prilozhen., 2008, Volume 42, Issue 1, Pages 78–82 (Mi faa2892)

Brief communications

Linear Extensions Associated with Abstract Functional Operators

A. B. Antonevichab, I. Yu. Trubnikova

a Belarusian State University
b University of Bialystok

Abstract: Abstract functional operators are defined as elements of a $C^*$-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 $\widehat{T}\colon a \to TaT^{-1}$ is an automorphism of $A$ and the set of finite sums $\sum a_kT^k$, $a_k\in A$, is norm dense in $B$.
We give a new construction of a linear extension associated with the abstract weighted shift operator $aT$ and 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.

Keywords: $C^*$-algebra, functional operator, weighted shift operator, spectrum of an operator, linear extension, hyperbolicity

DOI: https://doi.org/10.4213/faa2892

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English version:
Functional Analysis and Its Applications, 2008, 42:1, 65–68

Bibliographic databases:

UDC: 517.938

Citation: A. B. Antonevich, I. Yu. Trubnikov, “Linear Extensions Associated with Abstract Functional Operators”, Funktsional. Anal. i Prilozhen., 42:1 (2008), 78–82; Funct. Anal. Appl., 42:1 (2008), 65–68

Citation in format AMSBIB
\Bibitem{AntTru08} \by A.~B.~Antonevich, I.~Yu.~Trubnikov \paper Linear Extensions Associated with Abstract Functional Operators \jour Funktsional. Anal. i Prilozhen. \yr 2008 \vol 42 \issue 1 \pages 78--82 \mathnet{http://mi.mathnet.ru/faa2892} \crossref{https://doi.org/10.4213/faa2892} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2423980} \zmath{https://zbmath.org/?q=an:1167.47034} \transl \jour Funct. Anal. Appl. \yr 2008 \vol 42 \issue 1 \pages 65--68 \crossref{https://doi.org/10.1007/s10688-008-0007-5} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000255229000007} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-41549158198}