Smooth bump functions and geometry of Banach spaces

R. Deville; G. Godefroy; V. Zizler

doi:10.1112/S0025579300007075

Smooth bump functions and geometry of Banach spaces

R. Deville
, G. Godefroy
, V. Zizler

Research output: Contribution to journal › Article › peer-review

Abstract

Norms with moduli of smoothness of power type are constructed on spaces with the Radon-Nikodym property that admit pointwise Lipschitz bump functions with pointwise moduli of smoothness of power type. It is shown that no norms with pointwise moduli of rotundity of power type can exist on nonsuperreflexive spaces. A new smoothness characterization of spaces isomorphic to Hilbert spaces is given.

Original language	English (US)
Pages (from-to)	305-321
Number of pages	17
Journal	Mathematika
Volume	40
Issue number	2
DOIs	https://doi.org/10.1112/S0025579300007075
State	Published - 1993
Externally published	Yes

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title = "Smooth bump functions and geometry of Banach spaces",

abstract = "Norms with moduli of smoothness of power type are constructed on spaces with the Radon-Nikodym property that admit pointwise Lipschitz bump functions with pointwise moduli of smoothness of power type. It is shown that no norms with pointwise moduli of rotundity of power type can exist on nonsuperreflexive spaces. A new smoothness characterization of spaces isomorphic to Hilbert spaces is given.",

author = "R. Deville and G. Godefroy and V. Zizler",

note = "Acknowledgement. The first two authors would like to thank the Department of Mathematics, University of Alberta in Edmonton, where part of this work was completed, for its support and excellent working conditions during their stay there. The work was supported in part by a Canadian NSERC grant. The authors thank David Preiss and the referee for their suggestions for improvement of this paper, in particular for a new proof of Lemma III.6, which is included.",

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doi = "10.1112/S0025579300007075",

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AU - Deville, R.

AU - Godefroy, G.

AU - Zizler, V.

N1 - Acknowledgement. The first two authors would like to thank the Department of Mathematics, University of Alberta in Edmonton, where part of this work was completed, for its support and excellent working conditions during their stay there. The work was supported in part by a Canadian NSERC grant. The authors thank David Preiss and the referee for their suggestions for improvement of this paper, in particular for a new proof of Lemma III.6, which is included.

PY - 1993

Y1 - 1993

N2 - Norms with moduli of smoothness of power type are constructed on spaces with the Radon-Nikodym property that admit pointwise Lipschitz bump functions with pointwise moduli of smoothness of power type. It is shown that no norms with pointwise moduli of rotundity of power type can exist on nonsuperreflexive spaces. A new smoothness characterization of spaces isomorphic to Hilbert spaces is given.

AB - Norms with moduli of smoothness of power type are constructed on spaces with the Radon-Nikodym property that admit pointwise Lipschitz bump functions with pointwise moduli of smoothness of power type. It is shown that no norms with pointwise moduli of rotundity of power type can exist on nonsuperreflexive spaces. A new smoothness characterization of spaces isomorphic to Hilbert spaces is given.

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DO - 10.1112/S0025579300007075

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VL - 40

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JO - Mathematika

JF - Mathematika

IS - 2

ER -

Smooth bump functions and geometry of Banach spaces

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