Ji 氏のアブストラクト

Title: Gaussian White Noise Operators

Abstract: 

 Based on the topological isomorphisms induced by the kernel theorem and by second quantization, we introduce a quantization of (classical) operators on white noise functionals.

 By applying the quantization to a Gaussian white noise functional, we construct Gaussian white noise operators.

 We also introduce a notion of positivity for generalized operators from a locally convex space into its dual space and discuss the factorization property of such positive generalized operators from a Fréchet space into its dual space. 

 Then we characterize the positivity of the Gaussian white noise operators. Using the coherent state representation of white noise functionals and white noise operators, we establish a trace formula for trace-class operators on Boson Fock space and discuss sufficient conditions for Gaussian white noise operators to be trace-class.