ℂ-convexity in infinite-dimensional Banach spaces and applications to Kergin interpolation
We investigate the concepts of linear convexity and ℂ-convexity in 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 X...
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| Format: | Article |
| Language: | English |
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Hindawi Limited
2006-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/IJMMS/2006/80846 |