C-convexity in infinite-dimensional Banach spaces and applications to Kergin interpolation
2006 (English)In: International journal of mathematics and mathematical sciences, ISSN 0161-1712, E-ISSN 1687-0425, Vol. 2006Article in journal (Refereed) Published
We investigate the concepts of linear convexity and C-convexityin complex Banach spaces. The main result is that any C-convex domain is necessarily linearly convex. This is a complex version of the Hahn-Banach theorem, since it means the following: given a C-convex domain Ω in the Banach space Xand a point p∉Ω, there is a complex hyperplane through p that does not intersect Ω. We also prove that linearly convex domains are holomorphically convex, and that Kergin interpolation can be performed on holomorphic mappings defined in C-convex domains.
Place, publisher, year, edition, pages
Hindawi Publishing Corporation, 2006. Vol. 2006
IdentifiersURN: urn:nbn:se:kth:diva-66554DOI: 10.1155/IJMMS/2006/80846OAI: oai:DiVA.org:kth-66554DiVA: diva2:484307
QC 201202032012-01-262012-01-262012-02-03Bibliographically approved