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

Masaru Nishihara and Kwang Ho Shon

Abstract and Applied Analysis, 2014, vol. 2014, issue 1

Abstract: 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).

Date: 2014
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https://doi.org/10.1155/2014/795016

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:795016

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