Pro-Banach代数诱导交叉积
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摘要
以具有有界左逼近单位元的pro-Banach代数,局部紧群及群在代数上强连续作用为基础,定义了pro-Banach代数动力系统及与之相关的pro-Banach交叉积和pro-Banach诱导交叉积,并且证明了在紧群条件下,pro-Banach交叉积和pro-Banach诱导交叉积是同构的。
The definitions of pro-Banach algebra dynamcial systems,pro-Banach crossed products and pro-Banach algebra reduced crossed products were introduced based on the concepts ofpro-Banach algebras with a bounded approximate left identity,the locally compact groups and thestrong continuous actions of group on pro-Banach algebra.It was proved that the pro-Banach crossed product algebras and the pro-Banach reduced crossed product algebras associated with the given pro-Banach algebra dynamical systems are isomorphic when the group is compact.
The definitions of pro-Banach algebra dynamcial systems,pro-Banach crossed products and pro-Banach algebra reduced crossed products were introduced based on the concepts ofpro-Banach algebras with a bounded approximate left identity,the locally compact groups and thestrong continuous actions of group on pro-Banach algebra.It was proved that the pro-Banach crossed product algebras and the pro-Banach reduced crossed product algebras associated with the given pro-Banach algebra dynamical systems are isomorphic when the group is compact.
引文
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[13] LI D,XU S Z.Banach algebra dynamical system[J].Chin Ann Math,2014,35B(2):285-300.
[2] ZELLER-MEIER G.Produits croise′s d′une C*-algebras par un groupe d′automor-phismes[J].J.Math.Pures Appl.,1968,47(9):101-239.
[3] JOITA M.Crossed products of locally C*-algebras[J].Rocky Mountain J.Math.,2007,37(5):1623-1644.
[4] JOITA M.Pro-Banach dynamical systems with C*-crossed product[J].J.Math.Anal.Appl.,2011,377(1):428-434.
[5] JOITA M.Crossed prducts of pro-C*-algebras and Hilbert pro-C*-modules[J].Bulletin of the Malaysian Mathematical Sciences Society,2015,38(3):1-13.
[6] 杨新兵,方小春.C*-代数交叉积上的渐近同态[J].数学进展,2016,45(4):572-580.
[7] 王中华,张建华.多重C～*-动力系统在Hilbert C～*-模上的膨胀 [J].数学学报(中文版),2016,59(6):859-864.
[8] WILLIAMS D P.Crossed products of C*-algebras[M].Rhode Island:American Mathematical Society,2007.
[9] WORTEL M R.Group representations in Banach spaces and Banach lattices[D].Leiden,The Netherlands:Leiden University ,2012.
[10] MESSERSCHMIDT H J M.Positive representations on ordered Banach spaces[D].Leiden,The Netherlands:Leiden University ,2013.
[11] HUANG L Z,LU F Y .Reduced crossed products associated with Banach algebra dynamical systems[J].Integr Equ Oper Theory,2016,84 (4):451-462.
[12] 黄利忠.Banach代数交叉积的万有性质[J].扬州大学学报(自然科学版),2017,20(1):13-17.
[13] LI D,XU S Z.Banach algebra dynamical system[J].Chin Ann Math,2014,35B(2):285-300.