Abstract Let X be a complex Banach space and denote by Fᵖ_ (X) F α p (X) and F^w, p_ (X) F α w, p (X) the X -valued Fock spaces of entire functions f such that f (z) e^- {2|z|²} Lᵖ (dA) ‖ f (z) ‖ e - α 2 | z | 2 ∈ L p (d A) and x^* (f (z) ) e^- {2|z|²} Lᵖ (dA) x ∗ (f (z) ) e - α 2 | z | 2 ∈ L p (d A) for any x^* X^* x ∗ ∈ X ∗, respectively. For Hilbert-valued functions, it is shown that F²_ (H) =F^w, 2_ (H) F α 2 (H) = F α w, 2 (H) if and only if H is finite dimensional and also that <jats: tex-math
Blasco et al. (Thu,) studied this question.