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Displaying similar documents to “A Note on cotype of smooth spaces.”

On uniformly Gâteaux smooth C ( n ) -smooth norms on separable Banach spaces

Marián J. Fabián, Václav Zizler (1999)

Czechoslovak Mathematical Journal

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Every separable Banach space with C ( n ) -smooth norm (Lipschitz bump function) admits an equivalent norm (a Lipschitz bump function) which is both uniformly Gâteaux smooth and C ( n ) -smooth. If a Banach space admits a uniformly Gâteaux smooth bump function, then it admits an equivalent uniformly Gâteaux smooth norm.

Extension of smooth subspaces in Lindenstrauss spaces

V. P. Fonf, P. Wojtaszczyk (2014)

Studia Mathematica

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It follows from our earlier results [Israel J. Math., to appear] that in the Gurariy space G every finite-dimensional smooth subspace is contained in a bigger smooth subspace. We show that this property does not characterise the Gurariy space among Lindenstrauss spaces and we provide various examples to show that C(K) spaces do not have this property.

Smooth renormings of the Lebesgue-Bochner function space L¹(μ,X)

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.