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2014 The Tensor Product Representation of Polynomials of Weak Type in a DF-Space
Masaru Nishihara, Kwang Ho Shon
Abstr. Appl. Anal. 2014: 1-7 (2014). DOI: 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 pP(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 pP(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).


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Masaru Nishihara. Kwang Ho Shon. "The Tensor Product Representation of Polynomials of Weak Type in a DF-Space." Abstr. Appl. Anal. 2014 1 - 7, 2014.


Published: 2014
First available in Project Euclid: 6 October 2014

zbMATH: 07023088
MathSciNet: MR3193547
Digital Object Identifier: 10.1155/2014/795016

Rights: Copyright © 2014 Hindawi

Vol.2014 • 2014
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