Open Access

# Categories of unbounded operators

### Abstract

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.

### Article Information

 Title Categories of unbounded operators Source Methods Funct. Anal. Topology, Vol. 24 (2018), no. 1, 71-81 MathSciNet MR3783819 Milestones Received 12/09/2017 Copyright The Author(s) 2018 (CC BY-SA)

### Authors Information

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

### Citation Example

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

### BibTex

@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 = {http://mfat.imath.kiev.ua/article/?id=1026},
}

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