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.