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 $ mathcal{A} $ into a Hilbert $ mathcal{A} $-module $ E $. We introduce frames with bounds in pro-C*-algebra $ mathcal{A} $. New frames in Hilbert modules over pro-C*-algebras are called standard $ ast $-frames of multipliers. Meanwhile, we study several useful properties of standard $ ast $-frames in Hilbert modules over pro-C*-algebras and investigate conditions that under which the sequence ${ { {h_i} }_{i in I} }$ is a standard $ ast $-frame of multipliers for Hilbert modules over pro-C*-algebras. Also the effect of operators on standard $ ast $-frames of multipliers for $ E $ is examined. Finally, compositions of standard $ ast $-frames in Hilbert modules over pro-C*-algebras are studied.

Keywords:

Hilbert modules over pro-C*-algebras , Standard $ ast $-frame of multipliers , $ ast $-frame operator , Pre-$ ast $-frame