The Tensor Product Representation of Polynomials of Weak Type in a DF-Space

Abstract EN

Let E and F be locally convex spaces over C and let P ( n E ; F ) be the space of all continuous n -homogeneous polynomials from E to F .

We denote by ⨂ n , s , π E the n -fold symmetric tensor product space of E endowed with the projective topology.

Then, it is well known that each polynomial p ∈ P ( n E ; F ) is represented as an element in the space L ( ⨂ n , s , π E ; F ) of all continuous linear mappings from ⨂ n , s , π E to F .

A polynomial p ∈ P ( n E ; F ) is said to be of weak type if, for every bounded set B of E , p | B is weakly continuous on B .

We denote by P w ( n E ; F ) the space of all n -homogeneous polynomials of weak type from E to F .

In this paper, in case that E is a DF space, we will give the tensor product representation of the space P w ( n E ; F ) .