Document Type : Research Paper
Authors
1 Department of Mathematics, Kerman Branch, Islamic Azad University, Kerman, Iran.
2 Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, 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.
Keywords
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