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

Journal of Linear and Topological Algebra

مقاله 1، دوره 08، شماره 01، اردیبهشت 2019، صفحه 1-10   

نوع مقاله: Research Paper

نویسندگان

M. Naroei Irani¹؛ A. Nazari^{* 2}

¹Department of Mathematics, Kerman Branch, Islamic Azad University, Kerman, Iran

²Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran

چکیده

‎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.

کلیدواژه‌ها

Hilbert modules over pro-C*-algebras‎؛ ‎standard frame of multipliers‎؛ ‎standard *-frame of multipliers‎؛ *-frame operator‎؛ ‎pre-*-frame operator

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