Semicrossed Products of Operator Algebras by Semigroups

Ebook Details


Kenneth R. Davidson, Adam Fuller, Evgenios T. A. Kakariadis

Year 2017
Pages 97
Publisher Amer Mathematical Society
Language en
ISBN 9781470423094
File Size 838.31 KB
File Format PDF
Download Counter 90
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Ebook Description

The authors examine the semicrossed products of a semigroup action by $*$-endomorphisms on a C*-algebra, or more generally of an action on an arbitrary operator algebra by completely contractive endomorphisms. The choice of allowable representations affects the corresponding universal algebra. The authors seek quite general conditions which will allow them to show that the C*-envelope of the semicrossed product is (a full corner of) a crossed product of an auxiliary C*-algebra by a group action. Their analysis concerns a case-by-case dilation theory on covariant pairs. In the process we determine the C*-envelope for various semicrossed products of (possibly nonselfadjoint) operator algebras by spanning cones and lattice-ordered abelian semigroups.