Department of Mathematics and Statistics, University of Missouri-Rolla, Rolla, MO 65409, USA. E-mail: bekkerm@umr.edu
AMS subject classification: Primary 47B99, Secondary 47B15.
We give a functional characterization of a nondensely defined Hermitian contractive operator A and its self-adjoint extension  with the same norm which are unitarily equivalent to their linear-fractional transformations. Special attention is paid to the case when the orthogonal complement of the domain of A is one-dimensional. An example of such an operator A is considered.
Nondensely defined Hermitian contraction, self-adjoint extension, extreme extension, invariant contraction
