Linear extensions associated with abstract functional operators
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 \(B\).
scientific article; zbMATH DE number 5519857