# 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.

**Keywords:**$C^*$-algebra, relations, $*$-algebra, embed, word

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