Displaying similar documents to “Idempotent operators on a finite chain.”

Maps on idempotent operators

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...

Residual implications and co-implications from idempotent uninorms

Daniel Ruiz, Joan Torrens (2004)

Kybernetika

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This paper is devoted to the study of implication (and co-implication) functions defined from idempotent uninorms. The expression of these implications, a list of their properties, as well as some particular cases are studied. It is also characterized when these implications satisfy some additional properties specially interesting in the framework of implication functions, like contrapositive symmetry and the exchange principle.