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Abstract

We study the functor ℓ2 from the category of partial injections to the category of Hilbert spaces. The former category is finitely accessible, and in both categories homsets are algebraic domains. The functor preserves daggers, monoidal structures, enrichment, and various (co)limits, but has no adjoints. Up to unitaries, its direct image consists precisely of the partial isometries, but its essential image consists of all continuous linear maps between Hilbert spaces.

Keywords

Hilbert Space Orthonormal Basis Inverse Semigroup Polar Decomposition Partial Isometry 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Chris Heunen
    • 1
  1. 1.Department of Computer ScienceUniversity of OxfordUK

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