Some Properties of $ ast $-frames in Hilbert Modules Over Pro-C*-algebras
Journal: Sahand Communications in Mathematical Analysis (Vol.16, No. 1)Publication Date: 2019-10-13
Authors : Mona Naroei Irani; Akbar Nazari;
Page : 105-117
Keywords : Hilbert modules over pro-C*-algebras; Standard $ ast $-frame of multipliers; $ ast $-frame operator; Pre-$ ast $-frame;
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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Last modified: 2019-10-14 16:37:35