International Journal of Theoretical Physics

, Volume 47, Issue 1, pp 245–251 | Cite as

Spectral Lattices

  • Jan Hamhalter


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.


Spectral order Spectral orthomorphism Spectral and projection lattices Range projection map 


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Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.Faculty of Electrical Engineering, Department of MathematicsCzech Technical UniversityPragueCzech Republic

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