1. Trace conditions for regular spectral behavior of vector-valued analytic functions
- Author
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Bart, H., Ehrhardt, T., and Silbermann, B.
- Subjects
- *
ANALYTIC functions , *BANACH algebras , *CAUCHY problem , *FREDHOLM operators , *IDEMPOTENTS , *VECTOR analysis , *SPECTRAL geometry - Abstract
Abstract: A new class of Banach algebra valued functions is identified for which the logarithmic residue with respect to a Cauchy domain vanishes (if and) only if the functions take invertible values in . Trace conditions and the extraction of elementary factors of the type play an important role. The class contains the Fredholm operator valued functions and the Banach algebra valued functions possessing a simply meromorphic resolvent as special instances. An example is given to show that new ground is covered and a long standing open problem is discussed from a fresh angle. [Copyright &y& Elsevier]
- Published
- 2009
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