Fock Representation Of Analytic Mappings And Their Applications To Quantum Stochastic Calculus

E-operators play an important role in quantum stochastic calculus.In this paper,We discuss the existence of bounded extensions,isometry extensions and Hilbert-Schmit extensions of E-operators.The main results are as follows:Firstly, we prove some results on multilinear mappings taking values in a Banach space. Secondly, we introduce the S-B condition,strongly S-B condition and H-S condition for Frechet analytic mappings and then prove some theorems on a special class of Frechet analytic mappings which satisfy the S-B condition,strongly S-B condition and H-S condition. Thirdly, we provide a criterion based on the W-transform for checking whether or not an operator defined only on the exponential vectors becomes a bounded linear operators,isometry operators or Hilbert-Schmit operators on the Fork space, and a sufficient and necessary condition to Fock representation of analytic mappings. Finally, as an application to quantum stochastic calculus, we make use of the above results to demonstrate interpretation Wiener and interpretation Poisson.