| 1. |
- de Jeu, Marcel, et al.
(författare)
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On the Banach *-algebra crossed product associated with a topological dynamical system
- 2012
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Ingår i: Journal of Functional Analysis. - : Elsevier BV. - 0022-1236. ; 262:11, s. 4746-4765
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Tidskriftsartikel (refereegranskat)abstract
- Given a topological dynamical system Sigma = (X, sigma), where X is a compact Hausdorff space and a a homeomorphism of X, we introduce the Banach *-algebra crossed product l(1) (E) most naturally associated with Sigma and initiate its study. It has a richer structure than its well investigated C*-envelope, as becomes evident from the possible existence of non-self-adjoint closed ideals. We link its ideal structure to the dynamics, determining when the algebra is simple, or prime, and when there exists a non-self-adjoint closed ideal. A structure theorem is obtained when X consists of one finite orbit, and the algebra is shown to be Hermitian if X is finite. The key lies in analysing the commutant of C(X) in the algebra, which is shown to be a maximal abelian subalgebra with non-zero intersection with each non-zero closed ideal. (C) 2012 Elsevier Inc. All rights reserved.
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| 2. |
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| 3. |
- Osaka, Hiroyuki, et al.
(författare)
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Monotone operator functions, gaps and power moment problem
- 2007
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Ingår i: Mathematica Scandinavica. - 0025-5521. ; 100:1, s. 161-183
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Tidskriftsartikel (refereegranskat)abstract
- The article is devoted to investigation of the classes of functions belonging to the gaps between classes Pn+1 (I) and P, (I) of matrix monotone functions for full matrix algebras of successive dimensions. In this paper we address the problem of characterizing polynomials belonging to the gaps P-n(I) Pn+1 (I) for bounded intervals L We show that solution of this problem is closely linked to solution of truncated moment problems, Hankel matrices and Hankel extensions. Namely, we show that using the solutions to truncated moment problems we can construct continuum many polynomials in the gaps. We also provide via several examples some first insights into the further problem of description of polynomials in the gaps that are not coming from the truncated moment problem. Also, in this article, we deepen further in another way into the structure of the classes of matrix monotone functions and of the gaps between them by considering the problem of position in the gaps of certain interesting subclasses of matrix monotone functions that appeared in connection to interpolation of spaces and in a proof of the Lowner theorem on integral representation of operator monotone functions.
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| 4. |
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| 5. |
- Silvestrov, Sergei, et al.
(författare)
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Operator convex functions over C*-algebras
- 2010
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Ingår i: Proceedings of the Estonian Academy of Sciences. - : Estonian Academy Publishers. - 1736-7530 .- 1736-6046. ; 59:1, s. 48-52
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Tidskriftsartikel (refereegranskat)abstract
- In this short note we give an exact characterization of C*-algebras that have the class of convex functions. More precisely, we give a convexity characterization of subhomogeneous C*-algebras. We use these results to generalize the single function based convexity conditions for commutativity of a C*-algebra to the single function based convexity conditions for subhomogeneity.
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| 6. |
- Silvestrov, Sergei, et al.
(författare)
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Topological dynamical systems of type I
- 2002
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Ingår i: Expositiones Mathematicae. - 0723-0869. ; 20:2, s. 117-142
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Tidskriftsartikel (refereegranskat)abstract
- The equivalence of existence of a Borel section to nonexistence of recurrent aperiodic points for homeomorphisms of locally compact topological spaces is proved using the theory of C*-algebras.
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| 7. |
- Svensson, Christian, et al.
(författare)
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On the commutant of C(X) in C*-crossed products by Z and their representations
- 2009
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Ingår i: Journal of Functional Analysis. - : Elsevier BV. - 0022-1236. ; 256:7, s. 2367-2386
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Tidskriftsartikel (refereegranskat)abstract
- For the C*-crossed product C*(Sigma) associated with an arbitrary topological dynamical system Sigma = (X, sigma), we provide a detailed analysis of the commutant, in C*(Sigma), of C(X) and the commutant of the image of C(X) under an arbitrary Hilbert space representation (pi) over tilde of C*(E), In particular, we give a concrete description of these commutants, and also determine their spectra. We show that, regardless of the system E, the commutant of C(X) has non-zero intersection with every non-zero, not necessarily closed or self-adjoint, ideal of C*(Z). We also show that the corresponding statement holds true for the commutant of (pi) over tilde (C(X)) tinder the assumption that a certain family of pure states of (pi) over tilde (C*(Z)) is total. Furthermore we establish that, if C(X) subset of C(X)', there exist both a C*-Kibalgebra properly between C(X) and C(X)' which has the aforementioned intersection property, and such a C*-subalgebra which does not have this properly. We also discuss existence of* a projection of norm one from C*(Sigma) onto the commutant of C(X). (c) 2009 Elsevier Inc. All rights reserved.
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