462 C. Lifting Theorems
Remark C.5. Though one can almost always get around it by working
locally, a convenient generalization is available when the ideal is nuclear.
Namely, we can take E = B / J in ( 3) provided that B / J is separable and J
is nuclear. The proof of this needs a variant of Lemma 0.2 and is found in
[59].
References. Theorem 0.3 was proved in [38], but our proof follows [11].
Theorem 0.4 is from [59].