Multismoothness in Banach spaces.
Lin, Bor-Luh, Rao, T.S.S.R.K. (2007)
International Journal of Mathematics and Mathematical Sciences
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Lin, Bor-Luh, Rao, T.S.S.R.K. (2007)
International Journal of Mathematics and Mathematical Sciences
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M. Fabián, V. Zizler (1999)
Extracta Mathematicae
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Baronti, Marco, Papini, Pier Luigi (1992)
Mathematica Pannonica
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Marián J. Fabián, Václav Zizler (1999)
Czechoslovak Mathematical Journal
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Every separable Banach space with -smooth norm (Lipschitz bump function) admits an equivalent norm (a Lipschitz bump function) which is both uniformly Gâteaux smooth and -smooth. If a Banach space admits a uniformly Gâteaux smooth bump function, then it admits an equivalent uniformly Gâteaux smooth norm.
Marián Fabian, Sebastián Lajara (2012)
Studia Mathematica
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We show that, if μ is a probability measure and X is a Banach space, then the space L¹(μ,X) of Bochner integrable functions admits an equivalent Gâteaux (or uniformly Gâteaux) smooth norm provided that X has such a norm, and that if X admits an equivalent Fréchet (resp. uniformly Fréchet) smooth norm, then L¹(μ,X) has an equivalent renorming whose restriction to every reflexive subspace is Fréchet (resp. uniformly Fréchet) smooth.
Marina Marchisio (2006)
Bollettino dell'Unione Matematica Italiana
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We build a 54- (114-) dimensional family of smooth unirational quartic 3- (4-) folds.
Niculescu, Constantin P., Rădulescu, Vicenţiu (1996)
Annales Academiae Scientiarum Fennicae. Series A I. Mathematica
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Robert Deville, Vaclav E. Zizler (1988)
Manuscripta mathematica
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W. Waliszewski (1981)
Colloquium Mathematicae
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Park, Chun-Kee, Min, Won Keun, Kim, Myeong Hwan (2003)
International Journal of Mathematics and Mathematical Sciences
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V. Klee (1969)
Studia Mathematica
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Jean-Pierre Rosay (1986)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Vladimir Kadets, Varvara Shepelska, Dirk Werner (2008)
Bulletin of the Polish Academy of Sciences. Mathematics
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We consider a general concept of Daugavet property with respect to a norming subspace. This concept covers both the usual Daugavet property and its weak* analogue. We introduce and study analogues of narrow operators and rich subspaces in this general setting and apply the results to show that a quotient of L₁[0,1] by an ℓ₁-subspace need not have the Daugavet property. The latter answers in the negative a question posed to us by A. Pełczyński.