This paper gives the concept of the reduced pro-Banach algebra crossed product associated with inversely pro-Banach algebra dynamical system,and shows that the reduced crossed product is an inverse limit of an inverse...This paper gives the concept of the reduced pro-Banach algebra crossed product associated with inversely pro-Banach algebra dynamical system,and shows that the reduced crossed product is an inverse limit of an inverse system of Banach algebra crossed products.Also,the authors show that if the locally compact group is amenable,then the crossed product and the reduced crossed product are isometrically isomorphic.展开更多
Let X={X_(p)}p∈Pbe a product system over a lattice ordered group(G,P)with coefficients in a C*-algebra A.In this paper,we study the reduced crossed product of the gauge coactionδof G on the Cuntz-Pimsner algebra NO_...Let X={X_(p)}p∈Pbe a product system over a lattice ordered group(G,P)with coefficients in a C*-algebra A.In this paper,we study the reduced crossed product of the gauge coactionδof G on the Cuntz-Pimsner algebra NO_(X)^(r).When X is a product system of Morita equivalence bimodules,we show that the reduced crossed product of the gauge coaction is Morita equivalent to the C*-algebra A.展开更多
Abstract This paper generalizes the C＊-dynamical system to the Banach algebra dynam- ical system （A, G, α） and define the crossed product A αG of a given Banach algebra dynamical system （A, G,α）. Then the re...Abstract This paper generalizes the C＊-dynamical system to the Banach algebra dynam- ical system （A, G, α） and define the crossed product A αG of a given Banach algebra dynamical system （A, G,α）. Then the representation of A α G is described when A ad- mits a bounded left approximate identity. In a natural way, the authors define the reduced crossed product A αG and discuss the question when A α G coincides with A αG.展开更多
基金supported by the National Natural Science Foundation of China(No.11971277)the Scientific Innovation Foundation of the Higher Education Institutions of Shanxi Province(Nos.2019L0742,2019L0747)+1 种基金the Science and Technology Plan Project of Datong City(Nos.2021155,2019156)the Doctoral Scientific Research Foundation of Shanxi Datong University(No.2015-B-09)
文摘This paper gives the concept of the reduced pro-Banach algebra crossed product associated with inversely pro-Banach algebra dynamical system,and shows that the reduced crossed product is an inverse limit of an inverse system of Banach algebra crossed products.Also,the authors show that if the locally compact group is amenable,then the crossed product and the reduced crossed product are isometrically isomorphic.
基金Wang was supported in part by NSF of China(Grant Nos.11871303,11971463,11671133)NSF of Shandong Province(Grant No.ZR2019MA039)Yuan was supported in part by NSF of China(Grant Nos.11871303,11871127,11971463)。
文摘Let X={X_(p)}p∈Pbe a product system over a lattice ordered group(G,P)with coefficients in a C*-algebra A.In this paper,we study the reduced crossed product of the gauge coactionδof G on the Cuntz-Pimsner algebra NO_(X)^(r).When X is a product system of Morita equivalence bimodules,we show that the reduced crossed product of the gauge coaction is Morita equivalent to the C*-algebra A.
基金supported by the National Natural Science Foundation of China(No.10971023)the Shanghai Natural Science Foundation of China(No.09ZR1402000)
文摘Abstract This paper generalizes the C＊-dynamical system to the Banach algebra dynam- ical system （A, G, α） and define the crossed product A αG of a given Banach algebra dynamical system （A, G,α）. Then the representation of A α G is described when A ad- mits a bounded left approximate identity. In a natural way, the authors define the reduced crossed product A αG and discuss the question when A α G coincides with A αG.
