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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

Full text: PDF file (191 kB)
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English version:
Functional Analysis and Its Applications, 2008, 42:1, 65–68

Bibliographic databases:

UDC: 517.938
Received: 25.08.2006

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
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\paper Linear Extensions Associated with Abstract Functional Operators
\jour Funktsional. Anal. i Prilozhen.
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\vol 42
\issue 1
\pages 78--82
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