Displaying similar documents to “Commutation theorems and generalized commutation relations”

Representation and duality for Hilbert algebras

Sergio Celani, Leonardo Cabrer, Daniela Montangie (2009)

Open Mathematics

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In this paper we introduce a special kind of ordered topological spaces, called Hilbert spaces. We prove that the category of Hilbert algebras with semi-homomorphisms is dually equivalent to the category of Hilbert spaces with certain relations. We restrict this result to give a duality for the category of Hilbert algebras with homomorphisms. We apply these results to prove that the lattice of the deductive systems of a Hilbert algebra and the lattice of open subsets of its dual Hilbert...