Electronic Resource
Springer
Integral equations and operator theory
19 (1994), S. 135-152
ISSN:
1420-8989
Keywords:
Primary 46H99
;
30G30
;
16A38
;
Secondary 16A32
;
93B99
;
45E05
;
47A53
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
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.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01206410
Permalink
| Library |
Location |
Call Number |
Volume/Issue/Year |
Availability |
