Page 1

Displaying 1 – 8 of 8

Showing per page

Banach spaces in which all multilinear forms are weakly sequentially continuous

Jesús Castillo, Ricardo García, Raquel Gonzalo (1999)

Studia Mathematica

We solve several problems in the theory of polynomials in Banach spaces. (i) There exist Banach spaces without the Dunford-Pettis property and without upper p-estimates in which all multilinear forms are weakly sequentially continuous: some Lorentz sequence spaces, their natural preduals and, most notably, the dual of Schreier's space. (ii) There exist Banach spaces X without the Dunford-Pettis property such that all multilinear forms on X and X* are weakly sequentially continuous; this gives an...

Banach spaces of homogeneous polynomials without the approximation property

Seán Dineen, Jorge Mujica (2015)

Czechoslovak Mathematical Journal

We present simple proofs that spaces of homogeneous polynomials on L p [ 0 , 1 ] and p provide plenty of natural examples of Banach spaces without the approximation property. By giving necessary and sufficient conditions, our results bring to completion, at least for an important collection of Banach spaces, a circle of results begun in 1976 by R. Aron and M. Schottenloher (1976).

Banach spaces which admit a norm with the uniform Kadec-Klee property

S. Dilworth, Maria Girardi, Denka Kutzarova (1995)

Studia Mathematica

Several results are established about Banach spaces Ӿ which can be renormed to have the uniform Kadec-Klee property. It is proved that all such spaces have the complete continuity property. We show that the renorming property can be lifted from Ӿ to the Lebesgue-Bochner space L 2 ( Ӿ ) if and only if Ӿ is super-reflexive. A basis characterization of the renorming property for dual Banach spaces is given.

Binormality of Banach spaces

Petr Holický (1997)

Commentationes Mathematicae Universitatis Carolinae

We study binormality, a separation property of spaces endowed with two topologies known in the real analysis as the Luzin-Menchoff property. The main object of our interest are Banach spaces with their norm and weak topologies. We show that every separable Banach space is binormal and the space is not binormal.

Currently displaying 1 – 8 of 8

Page 1