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.

10.22130/scma.2018.75253.328

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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