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Digitale Medien

Logarithmic residues in Banach algebras (1994)

Bart, H. ; Ehrhardt, T. ; Silbermann, B.

Springer

Integral equations and operator theory 19 (1994), S. 135-152

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ISSN: 1420-8989

Schlagwort(e): Primary 46H99 ; 30G30 ; 16A38 ; Secondary 16A32 ; 93B99 ; 45E05 ; 47A53

Quelle: Springer Online Journal Archives 1860-2000

Thema: Mathematik

Notizen: Abstract Letf be an analytic Banach algebra valued function and suppose that the contour integral of the logarithmic derivativef′f −1 around a Cauchy domainD vanishes. Does it follow thatf takes invertible values on all ofD? For important classes of Banach algebras, the answer is positive. In general, however, it is negative. The counterexample showing this involves a (nontrivial) zero sum of logarithmic residues (that are in fact idempotents). The analysis of such zero sums leads to results about the convex cone generated by the logarithmic residues.

Materialart: Digitale Medien

URL: http://dx.doi.org/10.1007/BF01206410

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