Conditionally convergent series in a uniformly smooth Banach space

The theorem of Steinitz on the form of the set of points which are sums of convergent rearrangements of a given series is extended to series $\sum x_k$ in the uniformly smooth Banach space $X$ with modulus of smoothness $\rho(t)$, satisfying the condition $\sum\rho(||x_k||)<\infty$.