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arXiv · 1501.04888

Partial orders on partial isometries

Stephan Ramon Garcia·Robert T. W. Martin·William T. Ross
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Abstract

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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Stephan Ramon Garcia, Robert T. W. Martin, William T. Ross. 2015-01-18. Partial orders on partial isometries. https://arxiv.org/abs/1501.04888

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