ON PURELY INFINITE C-ASTERISK-ALGEBRAS

We find conditions under which a quotient C*-algebra A/I of a purely infinite C*-algebra A becomes purely infinite. S. Zhang proved that if A is a sigma-unital, simple, purely infinite C*-algebra, then a hereditary C*-subalgebra A(x) is a stable or unital for each x of A+ . We prove the converse for a completely a-unital infinite simple C*-algebra.