Rotund renormings in spaces of bochner integrable functions
Result description
We show that if ? is a probability measure and X is a Banach space, then the Lebesgue-Bochner space L1(?,X) admits an equivalent norm which is rotund (uniformly rotund in every direction, locally uniformly rotund, or midpoint locally uniformly rotund) ifX does. We also prove that if X admits a uniformly rotund norm, then the space L1(?,X) has an equivalent norm whose restriction to every reflexive subspace is uniformly rotund. This is done via the Luxemburg norm associated to a suitable Orlicz function.
Keywords
The result's identifiers
Result code in IS VaVaI
Result on the web
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DOI - Digital Object Identifier
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Alternative languages
Result language
angličtina
Original language name
Rotund renormings in spaces of bochner integrable functions
Original language description
We show that if ? is a probability measure and X is a Banach space, then the Lebesgue-Bochner space L1(?,X) admits an equivalent norm which is rotund (uniformly rotund in every direction, locally uniformly rotund, or midpoint locally uniformly rotund) ifX does. We also prove that if X admits a uniformly rotund norm, then the space L1(?,X) has an equivalent norm whose restriction to every reflexive subspace is uniformly rotund. This is done via the Luxemburg norm associated to a suitable Orlicz function.
Czech name
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Czech description
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Classification
Type
Jx - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Result continuities
Project
GAP201/12/0290: Topological and geometrical properties of Banach spaces and operator algebras
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2015
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Journal of Convex Analysis
ISSN
0944-6532
e-ISSN
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Volume of the periodical
22
Issue of the periodical within the volume
4
Country of publishing house
DE - GERMANY
Number of pages
15
Pages from-to
1025-1039
UT code for WoS article
000369772300007
EID of the result in the Scopus database
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Result type
Jx - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP
BA - General mathematics
Year of implementation
2015