Displaying similar documents to “The bidual of the space of polynomials on a Banach space.”

Polynomials and geometry of Banach spaces.

Joaquín M. Gutiérrez, Jesús A. Jaramillo, José G. Llavona (1995)

Extracta Mathematicae

Similarity:

In this paper we survey a large part of the results on polynomials on Banach spaces that have been obtained in recent years. We mainly look at how the polynomials behave in connection with certain geometric properties of the spaces.

Algebras of real analytic functions: Homomorphisms and bounding sets

Peter Biström, Jesús Jaramillo, Mikael Lindström (1995)

Studia Mathematica

Similarity:

This article deals with bounding sets in real Banach spaces E with respect to the functions in A(E), the algebra of real analytic functions on E, as well as to various subalgebras of A(E). These bounding sets are shown to be relatively weakly compact and the question whether they are always relatively compact in the norm topology is reduced to the study of the action on the set of unit vectors in l ∞ of the corresponding functions in A ( l ∞ ) . These results are achieved by studying the homomorphisms...

Ideals of homogeneous polynomials and weakly compact approximation property in Banach spaces

Erhan Çalışkan (2007)

Czechoslovak Mathematical Journal

Similarity:

We show that a Banach space E has the weakly compact approximation property if and only if each continuous Banach-valued polynomial on E can be uniformly approximated on compact sets by homogeneous polynomials which are members of the ideal of homogeneous polynomials generated by weakly compact linear operators. An analogous result is established also for the compact approximation property.

Unconditionally convergent polynomials in Banach spaces and related properties.

M.ª Teresa Fernández Unzueta (1997)

Extracta Mathematicae

Similarity:

Our aim is to introduce a new notion of unconditionallity, in the context of polynomials in Banach spaces, that looks directly to the polynomial topology defined on the involved spaces. This notion allows us to generalize some well-known relations of duality that appear in the linear context.

Polynomial characterizations of Banach spaces not containing l.

Joaquín M. Gutiérrez (1991)

Extracta Mathematicae

Similarity:

Many properties of Banach spaces can be given in terms of (linear bounded) operators. It is natural to ask if they can also be formulated in terms of polynomial, holomorphic and continuous mappings. In this note we deal with Banach spaces not containing an isomorphic copy of l, the space of absolutely summable sequences of scalars.