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Compact open sets in duals and projections in L1-algebras of certain semi-direct product groups

Published online by Cambridge University Press:  24 October 2008

Karlheinz Gröchenig ,
Eberhard Kaniuth  and
Keith F. Taylor
Karlheinz Gröchenig
Affiliation:
Department of Mathematics, University of Connecticut, Storrs, CT 06269, U.S.A.
Eberhard Kaniuth
Affiliation:
Fachbereich Mathematik/Informatik, Universität Paderborn, D-W-4790 Paderborn, Germany
Keith F. Taylor
Affiliation:
Department of Mathematics, University of Saskatchewan, Saskatoon, Saskatchewan S7N OWO, Canada
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Extract

The main purpose of this paper is to study projections, that is, self-adjoint idempotents, in L1-algebras of semi-direct products G = ℝ ⋉ ℝd, d ≥ 2. We establish necessary and sufficient conditions for the existence of non-zero projections in terms of the action of ℝ on ℝd. In the cases where such projections exist, we describe minimal ones in detail.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 111 , Issue 3 , May 1992 , pp. 545 - 556
Copyright
Copyright © Cambridge Philosophical Society 1992

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