*-frames in Hilbert modules over pro-C*-algebras

Subject Areas : Functional analysis

M.  Naroei Irani ¹ (Department of Mathematics, Kerman Branch, Islamic Azad University, Kerman, Iran)
A.  Nazari ² (Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran)

Received: 2018-05-03 Accepted : 2018-08-07 Published : 2019-02-01

Keywords: *-frame operator&lrm, , &lrm, pre-*-frame operator, Hilbert modules over pro-C*-algebras‎, ‎standard frame of multipliers‎, ‎standard *-frame of multipliers‎,

Abstract :

‎In this paper‎, ‎by using the sequence of multipliers‎, ‎we introduce frames with algebraic bounds in Hilbert pro-$ C^* $-modules‎. ‎We investigate the relations between frames and $ \ast $-frames‎. ‎Some properties of $ \ast $-frames in Hilbert pro-$ C^* $-modules are studied‎. ‎Also‎, ‎we show that there exist two differences between $ \ast $-frames in Hilbert pro-$ C^* $-modules and Hilbert $ C^* $-modules‎. ‎Finally‎, ‎dual $ \ast $-frames in Hilbert pro-$ C^* $-modules are presented‎.

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