Ergodic Properties in Quantum Systems
W. Thirring (1992)
Recherche Coopérative sur Programme n°25
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W. Thirring (1992)
Recherche Coopérative sur Programme n°25
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Steven Zelditch (1994-1995)
Séminaire de théorie spectrale et géométrie
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Carlo Pandiscia (2014)
Confluentes Mathematici
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Using the Nagy dilation of linear contractions on Hilbert space and the Stinespring’s theorem for completely positive maps, we prove that any quantum dynamical system admits a dilation in the sense of Muhly and Solel which satisfies the same ergodic properties of the original quantum dynamical system.
M. Keane (1970-1971)
Publications mathématiques et informatique de Rennes
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V. A. Malyshev (1989)
Banach Center Publications
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Wolfgang Krieger (1971)
Inventiones mathematicae
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M. Lemańczyk (1987)
Compositio Mathematica
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Mieczysław Mentzen (1991)
Studia Mathematica
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Ergodic group extensions of a dynamical system with discrete spectrum are considered. The elements of the centralizer of such a system are described. The main result says that each invariant sub-σ-algebra is determined by a compact subgroup in the centralizer of a normal natural factor.
Robert H. Lohman (1974)
Colloquium Mathematicae
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T. K. Pal, M. Maiti (1977)
Matematički Vesnik
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Cabiria Andreian Cazacu (1981)
Annales Polonici Mathematici
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D. J. Grubb (2008)
Fundamenta Mathematicae
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A quasi-linear map from a continuous function space C(X) is one which is linear on each singly generated subalgebra. We show that the collection of quasi-linear functionals has a Banach space pre-dual with a natural order. We then investigate quasi-linear maps between two continuous function spaces, classifying them in terms of generalized image transformations.
V. Buonomano (1978)
Annales de l'I.H.P. Physique théorique
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Mahesh Nerurkar (2000)
Colloquium Mathematicae
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We construct continuous G-valued cocycles that are not cohomologous to any compact constant via a measurable transfer function, provided the underlying dynamical system is rigid and the range group G satisfies a certain general condition. For more general ergodic aperiodic systems, we also show that the set of continuous ergodic cocycles is residual in the class of all continuous cocycles provided the range group G is a compact connected Lie group. The first construction is based on...