Search

We study projections and injections between projective tensor products spaces or spaces of polynomials and we show that the example of a polynomial constructed in [4], that is neither p-dominated nor compact, can be identified with the projection map of the symmetric tensor product onto the space. Also we give a characterization of the weak and quasi approximation properties on symmetric tensor products. [ABSTRACT FROM AUTHOR]

Given a regular probability measure μ on a compact Hausdorff space, we explicitly describe the predual of the Banach space of continuous n-homogeneous polynomials on L p (μ) as the completion of a (explicit constructed) subspace of L p/n (μ) with respect to a (explicitly constructed) norm π p/n . An application to the factorization of dominated polynomials is provided. [ABSTRACT FROM AUTHOR]

The aim of this paper is to prove a stronger version of a conjecture posed earlier on the existence of nondominated scalar-valued $m$-homogeneous polynomials, $m geq 3$, on arbitrary infinite dimensional Banach spaces. [ABSTRACT FROM AUTHOR]

Abstract: We prove that, like in the linear case, there is a canonical prototype of a p-dominated homogeneous polynomial through which every p-dominated polynomial between Banach spaces factors. [Copyright &y& Elsevier]