Characterizations of spectral automorphisms and a Stone-type theorem in orthomodular lattices
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Caragheorgheopol, Dan
Tkadlec, Josef
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The notion of spectral automorphism of an orthomodular lattice was introduced
by Ivanov and Caragheorgheopol [3] to create an analogue of the Hilbert space spectral
theory in the abstract framework of orthomodular lattices. We develop the theory of spec-
tral automorphisms nding previously missing characterizations of spectral automorphisms,
discussing several examples and the possibility to construct such automorphisms in direct
products or horizontal sums of lattices. A factorization of the spectrum of a spectral auto-
morphism is found. The last part of the paper addresses the problem of the unitary time
evolution of a system from the point of view of the spectral automorphisms theory. An ana-
logue of the Stone theorem concerning strongly continuous one-parameter unitary groups is
given.
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