Helene Bommier-Hato: Little Hankel operators on a class of vector-valued Fock spaces

Abstract: For a separable Hilbert space \(\mathcal H\), we consider the vector valued Fock space \(F^2_{m,\alpha}( \mathcal H)\) of those holomorphic functions \(f:\C^d-> \mathcal H\) which are square integrable with respect to the measure e^{-\alpha|z|^{2m]}, \(m \geq 1, \alpha >0\).
I will present some properties of the space \(F^2_{\alpha}( \mathcal H)\) and some  properties of the little Hankel operator \(h_b\), of symbol \(b: \C^d-> \mathcal L( \mathcal H)\), defined on \(F^2_{\alpha}( \mathcal H)\).