Hankel operators over the complex Wiener space

摘要

This work introduces and investigates ( small) Hankel operators H-b on the Hilbert space of holomorphic, square integrableWiener functionals. A regularity condition on the symbol b, which guarantees the boundedness of H-b, is provided. The symbols b for which H-b is of Hilbert - Schmidt type are characterized, and a representation of Hb by an integral operator is given. The proofs employ the hypercontractivity of the Ornstein-Uhlenbeck semigroup, together with approximations by finitely many variables. These results extend known results from a finite-dimensional context.