Nonself-adjoint Semicrossed Products by Abelian Semigroups

作者：Fuller Adam Hanley^*

来源：Canadian Journal of Mathematics, 2013, 65(4): 768-782.

DOI：10.4153/CJM-2012-051-8

• semicrossed product
• crossed product
• C*-envelope
• dilations

Let S be the semigroup S = Sigma(circle plus k)(i=1) S-i, where for each i is an element of I, S-i is a countable subsemigroup of the additive semigroup R+ containing 0. We consider representations of S as contractions {T-s}(s is an element of S) on a Hilbert space with the Nica-covariance property: T-s*T-t = TtTs* whenever t Lambda s = 0. We show that all such representations have a unique minimal isometric Nica-covariant dilation. %26lt;br%26gt;This result is used to help analyse the nonself-adjoint semicrossed product algebras formed from Nica-covariant representations of the action of S on an operator algebra A by completely contractive endomorphisms. We conclude by calculating the C*-envelope of the isometric nonself-adjoint semicrossed product algebra (in the sense of Kakariadis and Katsoulis).

• 出版日期2013-8