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Spectral Lattices

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Abstract

Spectral orthomorphisms between the spectral lattices of JBW algebras which preserve the scales extend to Jordan homomorphisms for a large class of algebras. Spectral lattice homomorphism is automatically a σ-lattice homomorphism. The range projection map is, up to a Jordan homomorphism, the only natural map from the spectral lattice onto the projection lattice. Continuity of the range projection determines finiteness of the algebra in Murray–von Neumann comparison theory.

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  1. Faculty of Electrical Engineering, Department of Mathematics, Czech Technical University, Technicka 2, 166 27, Prague, 6, Czech Republic

    Jan Hamhalter

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  1. Jan Hamhalter
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Correspondence to Jan Hamhalter.

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Hamhalter, J. Spectral Lattices. Int J Theor Phys 47, 245–251 (2008). https://doi.org/10.1007/s10773-007-9464-5

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  • DOI: https://doi.org/10.1007/s10773-007-9464-5

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