Some Properties of $ ast $-frames in Hilbert Modules Over Pro-C*-algebras

Authors

Akbar Nazari Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran.

Mona Naroei Irani Department of Mathematics, Kerman Branch, Islamic Azad University, Kerman, Iran.

Abstract:

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.

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