This paper studies three natural pre-orders of increasing generality on the set of all completely non-unitary partial isometries with equal defect indices. We show that the problem of determining when one partial isometry is less than another with respect to these pre-orders is equivalent to the existence of a bounded (or isometric) multiplier between two natural reproducing kernel Hilbert spaces of analytic functions. For large classes of partial isometries these spaces can be realized as the well-known model subspaces and deBranges-Rovnyak spaces. This characterization is applied to investigate properties of these pre-orders and the equivalence classes they generate.
Copyright © 2015 American Mathematical Society.
The definitive version is available at: http://arxiv.org/abs/1501.04888
Ross, William T., Stephan Ramon Garcia, and Robert T. W. Martin. "Partial Orders on Partial Isometries." Journal of Operational Theory, 2015, 1-30.
Ross, William T.; Garcia, Stephan Ramon; and Martin, Robert T. W., "Partial Orders on Partial Isometries" (2015). Department of Math & Statistics Faculty Publications. 103.