alpha-completely positive maps of group systems and Krein module representations

作者：Heo Jaeseong^*

来源：Journal of Mathematical Analysis and Applications, 2014, 409(1): 544-555.

DOI：10.1016/j.jmaa.2013.07.047

• (Covariant) alpha-completely positive map on groups
• J-representation
• Group system
• Locally C*-algebra
• Krein module over locally C*-algebras
• Projective isometric J-representation

In this paper, we study (covariant) alpha-completely positive maps on group systems. We first introduce a notion of alpha-completely positive maps of groups into (locally) C*-algebras and show that bounded alpha-completely positive maps on discrete groups induce alpha-completely positive linear maps on group C*-algebras. We establish the (covariant) KSGNS type representation theorem for (covariant) alpha-completely positive maps of group systems into locally C*-algebras. These constructions provide a projective covariant J-representation of a group system into a locally C*-algebra.

• 出版日期2014-1-1