Journal of Operator Theory

Volume 41, Issue 2, Spring 1999 pp. 351-364.

Embedding

$*$ -algebras into

$C^*$ -algebras

Authors: Paul Tapper
Author institution: Department of Mathematics, University of Leeds, Leeds, LS2 9JT, U.K.

Summary: A definition is given for

$C^*$ -ideals related to embedding

$*$ -alge\-bras in

$C^*$ -algebras. The shrinking algorithm on words is defined and related to the question of which words algebraically generate

$C^*$ -ideals. It is proved that all words in the free unital

$*$ -algebra with one generator generate

$C^*$ -ideals. Finally, the

$C^*$ -ideals generated by some specific words are described.

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