Journal of Operator Theory

Volume 55, Issue 1, Winter 2006 pp. 213-222.

$C^*$-algebras generated by scaling elements

Authors: Takeshi Katsura
Author institution: Department of Mathematics, Hokkaido University, Kita 10, Nishi 8, Kita-Ku, Sapporo, 060-0810, Japan

Summary: We investigate $C^*$-algebras generated by scaling elements. We generalize the Wold decomposition and Coburn's theorem on isometries to scaling elements. We also completely determine when the $C^*$-algebra generated by a scaling element contains an infinite projection.

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