Journal of Operator Theory

Volume 33, Issue 2, Spring 1995 pp. 235-248.

Canonical *-endomorphisms and simple $C^*$-algebras

Authors: Marie Choda
Author institution:Department of Mathematics, Osaka Kyoiku University, Asahigaoka, Kashiwara 582, JAPAN

Summary: Canonical property for a unit preserving *-endomorphism $\gamma$ of a unital $C^*$-algebra $A$ and the extension algebra $\left\langle {A,\gamma } \right\rangle$ of $A$ via $\gamma$ are introduced through the method of the crossed products by *-endomorphisms. The relation between Cuntz's canonical *-endomorphisms and Ocneanu's canonical shifts are obtained.

Keywords: *-endomorphisms, simple, crossed product.

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