Convergence of operators with deficiency indices (k, k) and of their self-adjoint extensions.

We consider an abstract sequence { A n } n = 1 ∞ of closed symmetric operators on a separable Hilbert space H . It is assumed that all A n 's have equal deficiency indices (k, k) and thus self-adjoint extensions { B n } n = 1 ∞ exist and are parametrized by partial isometries { U n } n = 1 ∞ on H according to von Neumann's extension theory. Under two different convergence assumptions on the A n 's we give the precise connection between strong resolvent convergence of the B n 's and strong convergence of the U n 's. [ABSTRACT FROM AUTHOR]