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. © 2013 Springer-Verlag Berlin Heidelberg.
CITATION STYLE
Heunen, C. (2013). On the functor l2. Lecture Notes in Computer Science (Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 7860 LNCS, 107–121. https://doi.org/10.1007/978-3-642-38164-5_8
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