A Moment Characterization of BValued Generalized Functionals of White Noise

Kernel theorems are established for Banach spacevalued multilinear mappings. A moment characterization theorem for Banach spacevalued generalized functionals of white noise is proved by using the above kernel theorems. A necessary and sufficient condition in terms of moments is given for sequences of Banach space-valued generalized functionals of white noise to converge strongly. The integration is also discussed of functions valued in the space of Banach space-valued generalized functionals.