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

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  • Masaru Nishihara
  • Kwang Ho Shon

Abstract

Let and be locally convex spaces over and let be the space of all continuous -homogeneous polynomials from to . We denote by the -fold symmetric tensor product space of endowed with the projective topology. Then, it is well known that each polynomial is represented as an element in the space of all continuous linear mappings from to . A polynomial is said to be of weak type if, for every bounded set of , is weakly continuous on . We denote by the space of all -homogeneous polynomials of weak type from to . In this paper, in case that is a DF space, we will give the tensor product representation of the space .

Suggested Citation

  • Masaru Nishihara & Kwang Ho Shon, 2014. "The Tensor Product Representation of Polynomials of Weak Type in a DF-Space," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-7, March.
    • Handle: RePEc:hin:jnlaaa:795016
    DOI: 10.1155/2014/795016
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