Another version of “Exotic characterization of a commutative -algebra”.
Saworotnow, Parfeny P. (2005)
International Journal of Mathematics and Mathematical Sciences
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Saworotnow, Parfeny P. (2005)
International Journal of Mathematics and Mathematical Sciences
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Litvinov, G.L. (2005)
Zapiski Nauchnykh Seminarov POMI
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Ágnes Szendrei (1996)
Mathematica Slovaca
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Al-Moajil, Abdullah H. (1982)
International Journal of Mathematics and Mathematical Sciences
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Margalida Mas Grimalt, Joan Torrens, Tomasa Calvo, Marc Carbonell (1999)
Mathware and Soft Computing
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This work is devoted to find and study some possible idempotent operators on a finite chain L. Specially, all idempotent operators on L which are associative, commutative and non-decreasing in each place are characterized. By adding one smoothness condition, all these operators reduce to special combinations of Minimum and Maximum.
Tomáš Kepka, Petr Němec (2012)
Acta Universitatis Carolinae. Mathematica et Physica
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Robert W. Quackenbush (1974)
Colloquium Mathematicae
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David Stanovsky (2009)
Rendiconti del Seminario Matematico della Università di Padova
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Peter Šemrl (2007)
Banach Center Publications
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The set of all bounded linear idempotent operators on a Banach space X is a poset with the partial order defined by P ≤ Q if PQ = QP = P. Another natural relation on the set of idempotent operators is the orthogonality relation defined by P ⊥ Q ⇔ PQ = QP = 0. We briefly survey known theorems on maps on idempotents preserving order or orthogonality. We discuss some related results and open problems. The connections with physics, geometry, theory of automorphisms, and linear preserver...