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.

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Post-print Article

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Publisher Statement

Copyright © 2015 American Mathematical Society.

The definitive version is available at: http://arxiv.org/abs/1501.04888

Full Citation:

Ross, William T., Stephan Ramon Garcia, and Robert T. W. Martin. "Partial Orders on Partial Isometries." Journal of Operational Theory, 2015, 1-30.