DERIVATIONS OF OPERATORS ON HILBERT PRO-C*-BIMODULES

We study derivations on the algebra of operators on Hilbert pro-C*-bimodules. We show that if E is a Hilbert bimodule over a commutative pro-C*-algebra A, then every derivation on KA(E), compact operators on E, is zero. Moreover, if A is a commutative -C*-algebra then every derivation on LA(E), adjointable oper- ators on E, is zero. Also, we prove that if E is a full Hilbert module over a pro-C*-algebra A, then the innerness of derivations on KA(E) implies the innerness of derivations on LA E