The Tensor Product Representation of Polynomials of Weak Type in a DF-Space. (30th March 2014)

• Record Type: Journal Article
• Authors: Nishihara, Masaru; Shon, Kwang Ho
• Other Names: Chen Zong-Xuan Academic Editor.
• Is Part Of: Abstract and applied analysis. Volume 2014(2014)
• Publication Date: 2014-03-30
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Applied Mathematics; Mathematical Analysis; Periodicals; 515.05
• DOI: 10.1155/2014/795016
• Languages: English
• ISSNs: 1085-3375

Abstract

Abstract : 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 ) .