Frames of multipliers in tensor products of Hilbert modules over pro--algebras

Given a standard frame of multipliers { h n } n for a Hilbert A-module E and a standard frame of multipliers { t n } n for a Hilbert B-module F we construct a standard frame of multipliers for the external tensor product of E and F and for the inner tensor product of E and F using a non-degenerate pro- C * -morphism φ from A to the pro- C * -algebra of all adjointable module morphisms on F.