Silvia Lassalle

Homogeneous Orthogonally Additive Polynomials on Banach Lattices

The main result in this paper is a representation theorem for homogeneous orthogonally additive polynomials on Banach lattices. The representation theorem is used to study the linear span of the set of zeros of homogeneous real-valued orthogonally additive polynomials. It is shown that in certain lattices every element can be represented as the sum of two or three zeros or, at least, can be approximated by such sums. It is also indicated how these results can be used to study weak topologies induced by orthogonally additive polynomials on Banach lattices.

To what extent does the dual Banach spaceE′ determine the polynomials overE?

We show that under conditions of regularity, ifE′ is isomorphic toF′, then the spaces of homogeneous polynomials overE andF are isomorphic. Some subspaces of polynomials more closely related to the structure of dual spaces (weakly continuous, integral, extendible) are shown to be isomorphic in full generality.

E′ and its relation with vector-valued functions on E

We study the relation between different spaces of vector-valued polynomials and analytic functions over dual-isomorphic Banach spaces. Under conditions of regularity onE andF, we show that the spaces ofX-valuedn-homogeneous polynomials and analytic functions of bounded type onE andF are isomorphic wheneverX is a dual space. Also, we prove that many of the usual subspaces of polynomials and analytic functions onE andF are isomorphic without conditions on the involved spaces.

Orthogonally additive holomorphic functions of bounded type over C ( K )

It is known that all

On the polynomial Lindenstrauss theorem

k

Weaker relatives of the bounded approximation property for a Banach operator ideal

-homogeneous orthogonally additive polynomials

Some Results Concerning the Determination of the Polynomials on E by the Dual Space E

P

Orthogonally Additive Polynomials over C(K) are Measures—A Short Proof

over

The Banach ideal of A-compact operators and related approximation properties

C(K)

On p-compact mappings and the p-approximation property

are of the form