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Categories of unbounded operators


In this article we introduce the concept of an $LK^\ast$-algebroid, which is defined axiomatically. The main example of an $LK^\ast$-algebroid is the category of all subspaces of a Hilbert space and closed (not necessarily bounded) linear operators. We prove that for any $LK^\ast$-algebroid there is a faithful functor that respects its structure and maps it into this main example.

Key words: Unbounded operators, Gelfand-Naimark-Segal construction, algebroid.

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Article Information

TitleCategories of unbounded operators
SourceMethods Funct. Anal. Topology, Vol. 24 (2018), no. 1, 71-81
MathSciNet   MR3783819
Milestones  Received 12/09/2017
CopyrightThe Author(s) 2018 (CC BY-SA)

Authors Information

Paul D. Mitchener
University of Sheffield, Western Bank, Sheffield S10 2TN, UK

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Paul D. Mitchener, Categories of unbounded operators, Methods Funct. Anal. Topology 24 (2018), no. 1, 71-81.


@article {MFAT1026,
    AUTHOR = {Paul D. Mitchener},
     TITLE = {Categories of unbounded operators},
   JOURNAL = {Methods Funct. Anal. Topology},
  FJOURNAL = {Methods of Functional Analysis and Topology},
    VOLUME = {24},
      YEAR = {2018},
    NUMBER = {1},
     PAGES = {71-81},
      ISSN = {1029-3531},
  MRNUMBER = {MR3783819},
       URL = {},


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