Interpolating sequences for $H^{\mathrm{\infty }}(B_H)$

We prove that under the extended Carleson’s condition, a sequence $(x_n) \subset B_H$islinearinterpolatingfor$H^{\infty}(B_H)$ for an infinite dimensional Hilbert space H. In particular, we construct the interpolating functions for each sequence and find a bound for the constant of interpolation.