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Sibirskii Matematicheskii Zhurnal, 2006, Volume 47, Number 1, Pages 97–107 (Mi smj853)  
This article is cited in 39 scientific papers (total in 39 papers)

Automorphisms and derivations on a universally complete complex $f$-algebra

A. G. Kusraev

Institute of Applied Mathematics and Informatics, Vladikavkaz Scientific Centre, RAS
Full-text PDF (246 kB) Citations (39)
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Abstract: We establish that, in a universally complete complex $K$-space with a fixed multiplicative structure, the $\sigma$-distributivity of the base is equivalent to each of the following assertions: (1) every band preserving linear operator is order bounded; (2) there are no nonzero derivations; (3) every band preserving endomorphism is a band projection; (4) there are no nontrivial band preserving automorphisms.
Keywords: vector lattice, $f$-algebra, band preserving operator, derivation, automorphism.
Received: 27.06.2005
English version:
Siberian Mathematical Journal, 2006, Volume 47, Issue 1, Pages 77–85
DOI: https://doi.org/10.1007/s11202-006-0010-0
Bibliographic databases:
UDC: 517.98, 512.8
Language: Russian
Citation: A. G. Kusraev, “Automorphisms and derivations on a universally complete complex $f$-algebra”, Sibirsk. Mat. Zh., 47:1 (2006), 97–107; Siberian Math. J., 47:1 (2006), 77–85
Citation in format AMSBIB
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    • This publication is cited in the following 39 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Сибирский математический журнал Siberian Mathematical Journal
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