Abstract
Using families of irreducible Hilbert space representations as a tool, the theory of analytic Fredholm operator valued function is extended to a C∗-algebra setting. This includes a C∗-algebra version of Rouché’s Theorem known from complex function theory. Also, criteria for spectral regularity of C∗-algebras are developed. One of those, involving the (generalized) Calkin algebra, is applied to C∗-algebras generated by a non-unitary isometry.
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