Download Operator Structures and Dynamical Systems: July 21-25, 2008 by Marcel De Jeu, Sergei Silvestrov, Christian Skau, Jun PDF

By Marcel De Jeu, Sergei Silvestrov, Christian Skau, Jun Tomiyama

ISBN-10: 0821847473

ISBN-13: 9780821847473

This quantity includes the lawsuits of a Leiden Workshop on Dynamical structures and their accompanying Operator constructions which came about on the Lorentz middle in Leiden, The Netherlands, on July 21-25, 2008. those papers supply a landscape of selfadjoint and non-selfadjoint operator algebras linked to either noncommutative and commutative (topological) dynamical platforms and similar matters. Papers on normal concept, in addition to extra really good ones on symbolic dynamics and complicated dynamical structures, are integrated

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Additional resources for Operator Structures and Dynamical Systems: July 21-25, 2008 Lorentz Center, Leiden, the Netherlands Satellite Conference of Teh Fifth European Congress of Mathematics

Sample text

19. If the IFS {γi }di=1 satisfies the cograph separation condition then Oγ Od . Proof. If χGi is the characteristic function of Gi then it belongs to C(G) and we note that ψ(χGi ) = χi ∗ S where χi is the characteristic function of the cylinder i. 1, the elements Si = d1/2 χi ∗ S = d1/2 ψ(χGi ) are d isometries that satisfies the Cuntz relations and generates Od . 4. The case of inverse branches of a continuous function. In this subsection we suppose that there exists a continuous function γ : K → K such that γ ◦ γi = id for all i ∈ {1, .

C 0000 (copyright Society holder) c 2009 American Mathematical 1 39 40 2 K. R. G. E. DAVIDSON 2. Semicrossed Products Arveson [2] and Arveson–Josephson [3] were the first to consider nonselfadjoint operator algebras constructed from dynamical systems. They considered a homeomorphism σ of a compact Hausdorff space X which preserves a probability measure µ satisfying µ(O) > 0 for every non-empty open set O ⊂ X. Given such a system, one can define a representation of C(X) on L2 (µ) as multiplication operators, and define a unitary U f = f ◦ σ.

We let A = C(K), E = C(G) where G = ∪di=1 Gi with Gi {(x, y) ∈ K × K : x = γi } being the cographs in the terminology of [16]. The structure of C*-correspondence is given by (φ(a)ξb)(x, y) = a(x)ξ(x, y)b(y) and d ξ, η A (y) = ξ(γi (y), y)η(γi (y), y) i=1 for a, b ∈ A and ξ, η ∈ E. 6 ([16]). (E = C(G), φ) is a full C*-correspondence over A = C(K) and φ : A → L(E) is faithful and unital. Moreover, the Hilbert module norm is equivalent to the sup norm in C(G). 7. The Kajiwara-Watatani algebra OΓ associated to Γ is the Cuntz-Pimsner algebra associated to the C*-correspondence defined above.

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