Functional Analysis and Its Applications

, Volume 42, Issue 1, pp 65–68 | Cite as

Linear extensions associated with abstract functional operators

  • A. B. Antonevich
  • I. Yu. Trubnikov
Brief Communications


Abstract functional operators are defined as elements of a C*-algebra B with a structure consisting of a closed C*-subalgebra AB and a unitary element TB such that the mapping \(\hat T:a \to TaT^{ - 1} \) is an automorphism of A and the set of finite sums \(\sum {a_k T^k } ,a_k \in A\), 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.

Key words

C-algebra functional operator weighted shift operator spectrum of an operator linear extension hyperbolicity 


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Copyright information

© Springer Science+Business Media, Inc. 2008

Authors and Affiliations

  1. 1.Belarus State UniversityBelarus
  2. 2.Uniwersytet w BiałlymstokuPoland

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