Bulletin of the Australian Mathematical Society

Research Article

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

CAISHI WANGa1 c1, YULAN ZHOUa2, DECHENG FENGa3 and QI HANa4

a1 School of Mathematics and Information Science, Northwest Normal University, Lanzhou, Gansu 730070, PR China (email: wangcs@nwnu.edu.cn, cswangnwnu@163.com)

a2 School of Mathematics and Information Science, Northwest Normal University, Lanzhou, Gansu 730070, PR China (email: zhouylw@nwnu.edu.cn)

a3 School of Mathematics and Information Science, Northwest Normal University, Lanzhou, Gansu 730070, PR China (email: fengdc@nwnu.edu.cn)

a4 School of Mathematics and Information Science, Northwest Normal University, Lanzhou, Gansu 730070, PR China (email: hanqi1978@nwnu.edu.cn)

Abstract

Let xs1D4A9* 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:xs1D4A9*xs21A6X to have a factorization of the form Ψ=Txs2218xs2130, where xs2130 is the exponential mapping on xs1D4A9* and T:Γ(xs1D4A9*)xs21A6X is a continuous linear operator, where Γ(xs1D4A9*) denotes the Boson Fock space over xs1D4A9*. 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.

(Received May 09 2009)

2000 Mathematics subject classification

  • primary 60H40; secondary 46G20

Keywords and phrases

  • inductive limit;
  • B-valued analytic mapping;
  • Fock factorization;
  • white noise

Correspondence:

c1 For correspondence; e-mail: wangcs@nwnu.edu.cn, cswangnwnu@163.com

Footnotes

Supported by National Natural Science Foundation of China (10571065), Natural Science Foundation of Gansu Province (0710RJZA106) and NWNU-KJCXGC, PR China.