Some Properties of Ast-Frames in Hilbert Modules Over Pro-C*-Algebras

In this paper, by using the sequence of adjointable operators from pro-c*-algebra a into a hilbert a-module e. we introduce frames with bounds in pro-c*-algebra a. new frames in hilbert modules over pro-c*-algebras are called standard ∗-frames of multipliers. meanwhile, we study several useful properties of standard ∗-frames in hilbert modules over pro-c*-algebras and investigate conditions that under which the sequence {hi}i∈i is a standard ∗-frame of multipliers for hilbert modules over pro-c*-algebras. also the effect of operators on standard ∗-frames of multipliers for e is examined. finally, compositions of standard ∗-frames in hilbert modules over pro-c*-algebras are studied.