Some Properties of *-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 {h(i)}(i is an element of 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.