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

Abstract

We prove that under the extended Carleson's condition, a sequence $(x_n)\subset B_H$ is linear interpolating for $H^{\infty }(B_H)$ 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.

12 pages