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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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 |
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doaj-03a4355120c9450abe567194c53c5e042020-11-24T23:40:18ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252006-01-01200610.1155/IJMMS/2006/8084680846ℂ-convexity in infinite-dimensional Banach spaces and applications to Kergin interpolationLars Filipsson0Division of Mathematics, Royal Institute of Technology (KTH), Stockholm 100 44, SwedenWe 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 and 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.http://dx.doi.org/10.1155/IJMMS/2006/80846 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Lars Filipsson |
| spellingShingle |
Lars Filipsson ℂ-convexity in infinite-dimensional Banach spaces and applications to Kergin interpolation International Journal of Mathematics and Mathematical Sciences |
| author_facet |
Lars Filipsson |
| author_sort |
Lars Filipsson |
| title |
ℂ-convexity in infinite-dimensional
Banach spaces and
applications to Kergin interpolation |
| title_short |
ℂ-convexity in infinite-dimensional
Banach spaces and
applications to Kergin interpolation |
| title_full |
ℂ-convexity in infinite-dimensional
Banach spaces and
applications to Kergin interpolation |
| title_fullStr |
ℂ-convexity in infinite-dimensional
Banach spaces and
applications to Kergin interpolation |
| title_full_unstemmed |
ℂ-convexity in infinite-dimensional
Banach spaces and
applications to Kergin interpolation |
| title_sort |
ℂ-convexity in infinite-dimensional
banach spaces and
applications to kergin interpolation |
| publisher |
Hindawi Limited |
| series |
International Journal of Mathematics and Mathematical Sciences |
| issn |
0161-1712 1687-0425 |
| publishDate |
2006-01-01 |
| description |
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
and 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. |
| url |
http://dx.doi.org/10.1155/IJMMS/2006/80846 |
| work_keys_str_mv |
AT larsfilipsson cconvexityininfinitedimensionalbanachspacesandapplicationstokergininterpolation |
| _version_ |
1725510152649441280 |