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C-convexity in infinite-dimensional Banach spaces and applications to Kergin interpolation
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).ORCID iD: 0000-0003-1755-3640
2006 (English)In: International journal of mathematics and mathematical sciences, ISSN 0161-1712, E-ISSN 1687-0425, Vol. 2006Article in journal (Refereed) Published
Abstract [en]

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
National Category
Mathematical Analysis
URN: urn:nbn:se:kth:diva-66554DOI: 10.1155/IJMMS/2006/80846OAI: diva2:484307
QC 20120203Available from: 2012-01-26 Created: 2012-01-26 Last updated: 2012-02-03Bibliographically approved

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Filipsson, Lars
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