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.
Full Text
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},
}
