ℂ -convexity in infinite-dimensional Banach spaces and applications to Kergin interpolation

Lars Filipsson

International Journal of Mathematics and Mathematical Sciences, 2006, vol. 2006, 1-9

Abstract:

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 acomplex version of the Hahn-Banach theorem, since it means thefollowing: given a ℂ -convex domain Ω in the Banach space X and a point p ∉ Ω , there is a complex hyperplanethrough p that does not intersect Ω . We also prove thatlinearly convex domains are holomorphically convex, and thatKergin interpolation can be performed on holomorphic mappingsdefined in ℂ -convex domains.

Date: 2006
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:080846

DOI: 10.1155/IJMMS/2006/80846

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