Journal of Operator Theory
Volume 67, Issue 2, Spring 2012 pp. 379-395.
Semicrossed products and reflexivityAuthors: Evgenios T.A. Kakariadis
Author institution: Department of Mathematics, University of Athens, Panepistimioupolis, GR-157 84, Athens, Greece
Summary: Given a w*-closed unital algebra \A acting on H0 and a contractive w*-continuous endomorphism β of \A, there is a w*-closed (non-selfadjoint) unital algebra Z+¯×β\A acting on H0⊗ℓ2(Z+), called the w*-semicrossed product of \A with β. We prove that Z+¯×β\A is a reflexive operator algebra provided \A is reflexive and β is unitarily implemented, and that Z+¯×β\A has the bicommutant property if and only if so does \A. Also, we show that the w*-semicrossed product generated by a commutative C∗-algebra and a continuous map is reflexive.
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