Extension of linear operators and Lipschitz maps into -spaces.
It is proved that every operator from a weak*-closed subspace of into a space C(K) of continuous functions on a compact Hausdorff space K can be extended to an operator from to C(K).
A space of boundary values is constructed for the minimal symmetric operator generated by an infinite Jacobi matrix in the limit-circle case. A description of all maximal dissipative, accretive and selfadjoint extensions of such a symmetric operator is given in terms of boundary conditions at infinity. We construct a selfadjoint dilation of maximal dissipative operator and its incoming and outgoing spectral representations, which makes it possible to determine the scattering matrix of dilation....