Best approximations from Hilbert submanifolds (Q1081773)

The problems of existence, uniqueness and differentiability of best approximations from a Hilbert submanifold, i.e. a possibly \(\infty\)- dimensional immersed submanifold M of a separable Hilbert space H are considered. The main results are strengthenings and generalizations of results which are given in the finite dimensional case by \textit{T. J. Abatzoglou} [Pac. J. Math. 87, 233-244 (1980; Zbl 0443.41028); and in Approximation theory III, Proc. Conf. Hon. G. G. Lorentz, Austin/Tex. 1980, 151-156 (1980; Zbl 0501.41021)].