Logarithmic residues, Rouché's theorem, and spectral regularity: The C*-algebra case

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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