...-Entropy, ...-Capacity, and Approximative Dimension for containing Spaces of the Classes Hp, p < 1.
N. Yanagihara, Shin Kawase (1974)
Monatshefte für Mathematik
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N. Yanagihara, Shin Kawase (1974)
Monatshefte für Mathematik
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Elliott H. Lieb, Mary Beth Ruskai (1973)
Recherche Coopérative sur Programme n°25
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Elliott H. Lieb, Mary Beth Ruskai (1973)
Recherche Coopérative sur Programme n°25
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Bodo Volkmann, Anne Bertrand-Mathis (1989)
Monatshefte für Mathematik
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Franz Hofbauer (1980)
Monatshefte für Mathematik
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P. Tuyls (1998)
Banach Center Publications
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Last years, the search for a good theory of quantum dynamical entropy has been very much intensified. This is not only due to its usefulness in quantum probability but mainly because it is a very promising tool for the theory of quantum chaos. Nowadays, there are several constructions which try to fulfill this need, some of which are more mathematically inspired such as CNT (Connes, Narnhofer, Thirring), and the one proposed by Voiculescu, others are more inspired by physics such as...
Woo, C.H. (2000)
Electronic Journal of Differential Equations (EJDE) [electronic only]
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Robert Alicki (1998)
Banach Center Publications
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We construct an example of a noncommutative dynamical system defined over a two dimensional noncommutative differential manifold with two positive Lyapunov exponents equal to ln d each. This dynamical system is isomorphic to the quantum Bernoulli shift on the half-chain with the quantum dynamical entropy equal to 2 ln d. This result can be interpreted as a noncommutative analog of the isomorphism between the classical one-sided Bernoulli shift and the expanding map of the circle and...
Thomas Hudetz (1998)
Banach Center Publications
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We define a new quantum dynamical entropy for a C*-algebra automorphism with an invariant state (and for an appropriate 'approximating' subalgebra), which entropy is a 'hybrid' of the two alternative definitions by Connes, Narnhofer and Thirring resp. by Alicki and Fannes (and earlier, Lindblad). We report on this entropy's properties and on three examples.
Nobua Aoki (1979)
Monatshefte für Mathematik
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F. Blanchard, E. Glasner (1995)
Monatshefte für Mathematik
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Paul C. Shields, Robert M. Burton (1983)
Monatshefte für Mathematik
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Brian Marcus (1979)
Monatshefte für Mathematik
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