(apd)–property of C∗–algebras by Extensions of C∗–algebras with (apd)
نویسنده
چکیده
A unital C∗–algebra A is said to have the (APD)–property if every nonzero element in A has the approximate polar decomposition. Let J be a closed ideal of A. Suppose that J̃ and A/J have (APD). In this paper, we give a necessary and sufficient condition that makes A have (APD). Furthermore, we show that if RR(J ) = 0 and tsr(A/J ) = 1 or A/J is a simple purely infinite C∗–algebra, then A has (APD).
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