Abstract
We establish that, in a universally complete complex K-space with a fixed multiplicative structure, the σ-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.
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To Semen Samsonovich Kutateladze on occasion of his sixtieth birthday.
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Translated from Sibirskii Matematicheskii Zhurnal, Vol. 47, No. 1, pp. 97–107, January–February, 2006.
Original Russian Text Copyright © 2006 Kusraev A. G.
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Kusraev, A.G. Automorphisms and Derivations on a Universally Complete Complex f-Algebra. Sib Math J 47, 77–85 (2006). https://doi.org/10.1007/s11202-006-0010-0
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DOI: https://doi.org/10.1007/s11202-006-0010-0