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1 results

  • FOCK FACTORIZATION OF B-VALUED ANALYTIC MAPPINGS ON A HILBERT INDUCTIVE LIMIT

  • Part of
  • CAISHI WANG, YULAN ZHOU, DECHENG FENG, QI HAN
  • Journal:
    Bulletin of the Australian Mathematical Society / Volume 81 / Issue 2 / April 2010
    Published online by Cambridge University Press:
    05 October 2009, pp. 236-250
    Print publication:
    April 2010
    • Article
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  • Let 𝒩* be a Hilbert inductive limit and X a Banach space. In this paper, we obtain a necessary and sufficient condition for an analytic mapping Ψ:𝒩*↦X to have a factorization of the form Ψ=T∘ℰ, where ℰ is the exponential mapping on 𝒩* and T:Γ(𝒩*)↦X is a continuous linear operator, where Γ(𝒩*) denotes the Boson Fock space over 𝒩*. To prove this result, we establish some kernel theorems for multilinear mappings defined on multifold Cartesian products of a Hilbert space and valued in a Banach space, which are of interest in their own right. We also apply the above factorization result to white noise theory and get a characterization theorem for white noise testing functionals.