Dynamics, Wavelets, Commutants and Transfer Operators Satisfying Crossed Product Type Commutation Relations

2013 ◽  
pp. 273-293
Author(s):  
Sergei Silvestrov
Keyword(s):  
Product Type ◽  
Crossed Product ◽  
Commutation Relations ◽  
Transfer Operators

scholarly journals Crossed products by abelian semigroups via transfer operators

2009 ◽  
Vol 30 (4) ◽  
pp. 1147-1164 ◽  
Author(s):  
NADIA S. LARSEN
Keyword(s):  
Transfer Operator ◽  
Crossed Product ◽  
Crossed Products ◽  
Transfer Operators ◽  
Product Systems ◽  
Natural Notion

AbstractWe propose a generalization of Exel’s crossed product by a single endomorphism and a transfer operator to the case of actions of abelian semigroups of endomorphisms and associated transfer operators. The motivating example for our definition yields new crossed products, not obviously covered by familiar theory. Our technical machinery builds on Fowler’s theory of Toeplitz and Cuntz–Pimsner algebras of discrete product systems of Hilbert bimodules, which we need to expand to cover a natural notion of relative Cuntz–Pimsner algebras of product systems.

scholarly journals Crossed product of aC*-algebra by an endomorphism, coefficient algebras and transfer operators

2011 ◽  
Vol 202 (9) ◽  
pp. 1253-1283 ◽  
Author(s):  
Anatolii B Antonevich ◽  
Victor I Bakhtin ◽  
Andrei V Lebedev
Keyword(s):  
Crossed Product ◽  
Transfer Operators

Spectra for Infinite Tensor Product Type Actions of Compact Groups

1996 ◽  
Vol 48 (2) ◽  
pp. 330-342
Author(s):  
Elliot C. Gootman ◽  
Aldo J. Lazar
Keyword(s):  
Tensor Product ◽  
Compact Group ◽  
Abelian Groups ◽  
Product Type ◽  
Crossed Product ◽  
Compact Groups ◽  
Ideal Structure ◽  
Crossed Product Algebra ◽  
Product Algebra ◽  
The Ideal

AbstractWe present explicit calculations of the Arveson spectrum, the strong Arveson spectrum, the Connes spectrum, and the strong Connes spectrum, for an infinite tensor product type action of a compact group. Using these calculations and earlier results (of the authors and C. Peligrad) relating the various spectra to the ideal structure of the crossed product algebra, we prove that the topology of G influences the ideal structure of the crossed product algebra, in the following sense: if G contains a nontrivial connected group as a direct summand, then the crossed product algebra may be prime, but it is never simple; while if G is discrete, the crossed product algebra is simple if and only if it is prime. These results extend to compact groups analogous results of Bratteli for abelian groups. In addition, we exhibit a class of examples illustrating that for compact groups, unlike the case for abelian groups, the Connes spectrum and strong Connes spectrum need not be stable.

GENERALISED ARMENDARIZ PROPERTIES OF CROSSED PRODUCT TYPE

2015 ◽  
Vol 58 (2) ◽  
pp. 313-323
Author(s):  
LIANG ZHAO ◽  
YIQIANG ZHOU
Keyword(s):  
Semiprime Ring ◽  
Product Type ◽  
Crossed Product ◽  
Rigid Ring ◽  
Ordered Monoid ◽  
Armendariz Rings ◽  
Totally Ordered Monoid

AbstractLet R be a ring and M a monoid with twisting f:M × M → U(R) and action ω: M→ Aut(R). We introduce and study the concepts of CM-Armendariz and CM-quasi-Armendariz rings to generalise various Armendariz and quasi-Armendariz properties of rings by working on the context of the crossed product R*M over R. The following results are proved: (1) If M is a u.p.-monoid, then any M-rigid ring R is CM-Armendariz; (2) if I is a reduced ideal of an M-compatible ring R with M a strictly totally ordered monoid, then R/I being CM-Armendariz implies that R is CM-Armendariz; (3) if M is a u.p.-monoid and R is a semiprime ring, then R is CM-quasi-Armendariz. These results generalise and unify many known results on this subject.

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