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

• Autorzy: Marián Fabian , Sebastián Lajara
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 46E40: Spaces of vector- and operator-valued functions
• 46B20: Geometry and structure of normed linear spaces
• 46B03: Isomorphic theory (including renorming) of Banach spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2012
• Tom: 209
• Numer: 3
• Strony: 247-265

Daty

wydano

2012

Twórcy

autor

Marián Fabian

• Institute of Mathematics, Czech Academy of Sciences, Žitná 25, 115 67 Praha 1, Czech Republic

autor

Sebastián Lajara

• Departamento de Matemáticas, Escuela de Ingenieros Industriales, Universidad de Castilla-La Mancha, Campus Universitario, 02071 Albacete, Spain

Identyfikatory

DOI

10.4064/sm209-3-4