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

• Main Authors: Masaru Nishihara, Kwang Ho Shon
• Format: Article
• Language: English
• Published: Hindawi Limited 2014-01-01
• Series: Abstract and Applied Analysis
• Online Access: http://dx.doi.org/10.1155/2014/795016

Let E and F be locally convex spaces over C and let P(nE;F) be the space of all continuous n-homogeneous polynomials from E to F. We denote by ⨂n,s,πE the n-fold symmetric tensor product space of E endowed with the projective topology. Then, it is well known that each polynomial p∈P(nE;F) is represented as an element in the space L(⨂n,s,πE;F) of all continuous linear mappings from ⨂n,s,πE to F. A polynomial p∈P(nE;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 Pw(nE;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 Pw(nE;F).