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dc.contributor.authorDodds, Peter Gerard
dc.contributor.authorDodds, Theresa Kee-Yu
dc.contributor.authorSedaev, Alexander A
dc.contributor.authorSukochev, Fyodor Anatolievich
dc.date.accessioned2018-04-30T06:00:47Z
dc.date.available2018-04-30T06:00:47Z
dc.date.issued2004-01
dc.identifier.citationPeter G. Dodds, Theresa K. Dodds, Alexander A. Sedaev, and Fyodor A. Sukochev, “Local uniform convexity and Kadec-Klee type properties in -interpolation spaces I: General Theory,” Journal of Function Spaces and Applications, vol. 2, no. 2, pp. 125-173, 2004. doi:10.1155/2004/678358
dc.identifier.issn0972-6802
dc.identifier.urihttps://doi.org/10.1155/2004/678358
dc.identifier.urihttp://hdl.handle.net/2328/37956
dc.descriptionCopyright © 2004 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.en
dc.description.abstractWe present a systematic study of the interpolation of local uniform convexity and Kadec-Klee type properties in K-interpolation spaces. Using properties of the K-functional of J.Peetre, our approach is based on a detailed analysis of properties of a Banach couple and properties of a K-interpolation functional which guarantee that a given K-interpolation space is locally uniformly convex, or has a Kadec-Klee property. A central motivation for our study lies in the observation that classical renorming theorems of Kadec and of Davis, Ghoussoub and Lindenstrauss have an interpolation nature. As a partiular by-product of our study, we show that the theorem of Kadec itself, that each separable Banach space admits an equivalent locally uniformly convex norm, follows directly from our approach.
dc.language.isoenen
dc.publisherHindawien
dc.rightsCopyright © 2004 Hindawi Publishing Corporation.
dc.subjectBanach couple
dc.subjectK-Interpolation space
dc.subjectLocal uniform convexity
dc.subjectKadec-Klee property
dc.titleLocal uniform convexity and Kadec-Klee type properties in -interpolation spaces I: General Theoryen
dc.typeArticleen
dc.identifier.doihttps://doi.org/10.1155/2004/678358
dc.date.updated2018-04-26T09:01:37Z
dc.rights.holderHindawi Publishing Corporation.
dc.rights.licenseCC-BY


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