Noncommutative Mathematics for Quantum Systems
162 Noncommutative Mathematics for Quantum Systems is a (normal) isomorphism of the von Neumann algebraMand πω(M)′′=πω(M). Moreo ...
Quantum Dynamical Systems from the Point of View of Noncommutative Mathematics 163 right shift operators byR(Γ). Prove, using Th ...
164 Noncommutative Mathematics for Quantum Systems Theorem 2.5.1. Note that the above statements can be viewed as another way of ...
Quantum Dynamical Systems from the Point of View of Noncommutative Mathematics 165 Fix now a normal functionalγ∈M∗⊂M∗and define ...
166 Noncommutative Mathematics for Quantum Systems ̃s(γ,x) =γ(x)and thusx=Φ(x). These two facts combined show thatΦis an idempot ...
Quantum Dynamical Systems from the Point of View of Noncommutative Mathematics 167 pointwise (almost surely) to a function f if ...
168 Noncommutative Mathematics for Quantum Systems and 1 n n− 1 ∑ k= 0 αk(x)≤y, n∈N. The proof of the Maximal Lemma is based on ...
Quantum Dynamical Systems from the Point of View of Noncommutative Mathematics 169 Theorem 2.6.6 Let((Y,μ),T)be a measurable dyn ...
170 Noncommutative Mathematics for Quantum Systems it is easy to verify that Uψ∗δγ=δψ(γ), γ∈Γ. Further for anyγ,γ′∈Γ Uψ∗λγUψδγ′= ...
Quantum Dynamical Systems from the Point of View of Noncommutative Mathematics 171 Asγwas arbitrary, this implies thatξis suppor ...
172 Noncommutative Mathematics for Quantum Systems nlim→∞ 1 n n− 1 ∑ k= 0 ‖αk(x)y−yαk(x)‖ 2 =0. The last result is also proved i ...
References [AET] T. Austin, T. Eisner and T. Tao, Nonconventional ergodic averages and multiple recurrence for von Neumann dynam ...
174 References [DF] T. Downarowicz and B. Frej, Measure-theoretic and topological entropy of operators on function spaces,Ergodi ...
References 175 [Ra] I. Raeburn, “GraphC∗-algebras", CBMS Regional Conference Series in Mathematics, 103, Providence, RI, 2005. [ ...
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Index C∗-algebra, 122 commutative, 122 Cuntz-Krieger, 129 graph, 129, 146 nuclear, 137, 154 of a bitstream, 147 reduced group, 1 ...
178 Index of a bialgebra, 31 of a dual (semi-)group, 100 corepresentation, 44 contragredient, 45 irreducible, 44 non-degenerate, ...
Index 179 Hopf algebra, 32 joint distribution of a quantum stochastic process, 30 Kac type compact quantum group, 48 Kochen-Spec ...
180 Index topological pressure classical, 136 noncommutative, 140 transform Cauchy-Stieltjes, 55 Fourier, 46 reciprocal Cauchy-S ...
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