The Orthomodular Poset of Projections of A Symmetric Lattices |
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Authors: | Email author" target="_blank">Georges?ChevalierEmail author |
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Institution: | (1) InstitutGirardDesargues, UMR 5028, Mathématiques, Université Claude − Bernard LYON 1, 43, bd. du 11 novembre 1918, 69622 Villeurbannecedex, France |
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Abstract: | In a Hilbert space, there exists a natural correspondence between continuous projections and particular pairs of closed subspaces.
In this paper, we generalize this situation and associate to a symmetric lattice L a subset P(L) of L× L, called its projection poset. If L is the lattice of closed subspaces of a topological vector space then elements of P(L) correspond to continuous projections and we prove that automorphisms of P(L) are determined by automorphisms of the lattice L when this lattice satisfies some basic properties of lattices of closed subspaces.
Primary: 06C15, Secondary: 03G12 81P10. |
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Keywords: | orthomodular lattices symmetric lattices lattices of subspaces |
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