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  • Bulletin of the Australian Mathematical Society, Volume 81, Issue 2
  • April 2010, pp. 236-250

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

  • CAISHI WANG (a1), YULAN ZHOU (a2), DECHENG FENG (a3) and QI HAN (a4)
  • DOI: http://dx.doi.org/10.1017/S000497270900077X
  • Published online: 01 October 2009
Abstract
Abstract

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.

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Copyright
Corresponding author
For correspondence; e-mail: wangcs@nwnu.edu.cn, cswangnwnu@163.com
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Supported by National Natural Science Foundation of China (10571065), Natural Science Foundation of Gansu Province (0710RJZA106) and NWNU-KJCXGC, PR China.

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This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

[5]N. Obata , White Noise Calculus and Fock Space, Lecture Notes in Mathematics, 1577 (Springer, Berlin, 1994).

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Bulletin of the Australian Mathematical Society
  • ISSN: 0004-9727
  • EISSN: 1755-1633
  • URL: /core/journals/bulletin-of-the-australian-mathematical-society
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