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Spectral automorphisms in CB-effect algebras

In: Mathematica Slovaca, vol. 62, no. 6
Dan Caragheorgheopol
Detaily:
Rok, strany: 2012, 1173 - 1192
Kľúčové slová:
spectral automorphism, effect algebra, compression base, CB-effect algebra, spectral theory, effect algebra automorphism
O článku:
Spectral automorphisms have been introduced in [IVANOV, A.—CARAGHEORGHEOPOL, D.: \textit{Spectral automorphisms in quantum logics}, Internat. J. Theoret. Phys. \textbf{49} (2010), 3146–3152] in an attempt to construct, in the abstract framework of orthomodular lattices, an analogue of the spectral theory in Hilbert spaces. We generalize spectral automorphisms to the framework of effect algebras with compression bases and study their properties. Characterizations of spectral automorphisms as well as necessary conditions for an automorphism to be spectral are given. An example of a spectral automorphism on the standard effect algebra of a finite-dimensional Hilbert space is discussed and the consequences of spectrality of an automorphism for the unitary Hilbert space operator that generates it are shown. The last section is devoted to spectral families of automorphisms and their properties, culminating with the formulation and proof of a Stone type theorem (in the sense of Stone's theorem on strongly continuous one-parameter unitary groups — see, e.g. [REED, M.—SIMON, B.: \textit{Methods of Modern Mathematical Physics, Vol. I}, Acad. Press, New York, 1975]) for a group of spectral automorphisms.
Ako citovať:
ISO 690:
Caragheorgheopol, D. 2012. Spectral automorphisms in CB-effect algebras. In Mathematica Slovaca, vol. 62, no.6, pp. 1173-1192. 0139-9918. DOI: https://doi.org/10.2478/s12175-012-0072-3

APA:
Caragheorgheopol, D. (2012). Spectral automorphisms in CB-effect algebras. Mathematica Slovaca, 62(6), 1173-1192. 0139-9918. DOI: https://doi.org/10.2478/s12175-012-0072-3
O vydaní: