Trace conditions for regular spectral behavior of vector-valued analytic functions
SCIE
SCOPUS
- Title
- Trace conditions for regular spectral behavior of vector-valued analytic functions
- Authors
- Bart, H; Ehrhardt, T; Silbermann, B
- Date Issued
- 2009-04-15
- Publisher
- ELSEVIER SCIENCE INC
- Abstract
- A new class of Banach algebra valued functions is identified for which the logarithmic residue with respect to a Cauchy domain Delta vanishes (if and) only if the functions take invertible values in Delta. Trace conditions and the extraction of elementary factors of the type e - p + (lambda - alpha)p 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. (C) 2008 Elsevier Inc. All rights reserved.
- Keywords
- Logarithmic residue; Analytic vector-valued function; Elementary factor; Plain function; Idempotent; Annihilating family of idempotents; Resolving family of traces; Integer combination of idempotents; LOGARITHMIC RESIDUES; BANACH-ALGEBRAS; OPERATOR FUNCTIONS; MATRIX ALGEBRAS; IDEMPOTENTS; SUMS
- URI
- https://oasis.postech.ac.kr/handle/2014.oak/26357
- DOI
- 10.1016/J.LAA.2008.11.004
- ISSN
- 0024-3795
- Article Type
- Article
- Citation
- LINEAR ALGEBRA AND ITS APPLICATIONS, vol. 430, no. 89, page. 1945 - 1965, 2009-04-15
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