Noncommutative Mathematics for Quantum Systems
122 Noncommutative Mathematics for Quantum Systems Notational conventions For a subsetXof a Banach space the closed linear span ...
Quantum Dynamical Systems from the Point of View of Noncommutative Mathematics 123 The assumption of unitality of theC∗-algebras ...
124 Noncommutative Mathematics for Quantum Systems Definition 2.1.4 A quantum (or noncommutative) dynamical system is a pair (A, ...
Quantum Dynamical Systems from the Point of View of Noncommutative Mathematics 125 contractive). Another theorem due to Gelfand ...
126 Noncommutative Mathematics for Quantum Systems successfully implemented by Woronowicz ([Wo]) and led to the theory of compac ...
Quantum Dynamical Systems from the Point of View of Noncommutative Mathematics 127 is a dense∗-subalgebra ofON. We will be furth ...
128 Noncommutative Mathematics for Quantum Systems suppose thatXis a closed subset of a compact spaceY. What can be then said of ...
Quantum Dynamical Systems from the Point of View of Noncommutative Mathematics 129 (i) eachPvis an orthogonal projection, that i ...
130 Noncommutative Mathematics for Quantum Systems As in the case of Cuntz algebras, we will be interested in what follows in so ...
Quantum Dynamical Systems from the Point of View of Noncommutative Mathematics 131 (i) eachλγis unitary; (ii) for anyγ,γ′∈Γwe ha ...
132 Noncommutative Mathematics for Quantum Systems shift 2.2.1 Endomorphisms of Cuntz algebras and a quantum We will be interest ...
Quantum Dynamical Systems from the Point of View of Noncommutative Mathematics 133 Exercise 2.2.3 Check that the formula (2.2.2) ...
134 Noncommutative Mathematics for Quantum Systems 2.2.2 The shift transformation on a graphC∗-algebra LetΛ = (V,E) be a finite ...
Quantum Dynamical Systems from the Point of View of Noncommutative Mathematics 135 (and Sinai) in 1950s for measurable dynamical ...
136 Noncommutative Mathematics for Quantum Systems lim sup n→∞ 1 n logs(n,e) =lim sup n→∞ 1 n logNk+^1 +n =lim sup n→∞ n+k+ 1 n ...
Quantum Dynamical Systems from the Point of View of Noncommutative Mathematics 137 A ψ id //A Mn φ >> Further forΩ ⊂⊂Aande ...
138 Noncommutative Mathematics for Quantum Systems htα= sup e>0,Ω⊂⊂A lim sup n→∞ ( 1 n log rcp(Ω(n),e) ) (here and below we u ...
Quantum Dynamical Systems from the Point of View of Noncommutative Mathematics 139 φ([aij]ki,j= 1 ) = k ∑ i= 1 aiiφi, [aij]ki,j= ...
140 Noncommutative Mathematics for Quantum Systems Proposition 2.2.11 (Kolmogorov–Sinai property, [Vo]) LetAbe a nuclearC∗-algeb ...
Quantum Dynamical Systems from the Point of View of Noncommutative Mathematics 141 defines a natural notion of a ‘finite-dimensi ...
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