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Exact and Approximate Operator Parallelism

Published online by Cambridge University Press:  20 November 2018

Ali Zamani  and
Mohammad Sal Moslehian
Ali Zamani
Affiliation:
Department of PureMathematics, Center of Excellence in Analysis on Algebraic Structures (CEAAS), Ferdowsi University of Mashhad, Mashhad 91775, Iran. e-mail: zamani.ali85@yahoo.com, e-mail: moslehian@um.ac.ir e-mail: moslehian@member.ams.org
Mohammad Sal Moslehian
Affiliation:
Department of PureMathematics, Center of Excellence in Analysis on Algebraic Structures (CEAAS), Ferdowsi University of Mashhad, Mashhad 91775, Iran. e-mail: zamani.ali85@yahoo.com, e-mail: moslehian@um.ac.ir e-mail: moslehian@member.ams.org
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Abstract

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Extending the notion of parallelism we introduce the concept of approximate parallelism in normed spaces and then substantially restrict ourselves to the setting of Hilbert space operators endowed with the operator norm. We present several characterizations of the exact and approximate operator parallelism in the algebra $\mathbb{B}\left( H \right)$ of bounded linear operators acting on a Hilbert space $H$. Among other things, we investigate the relationship between the approximate parallelism and norm of inner derivations on $\mathbb{B}\left( H \right)$. We also characterize the parallel elements of a ${{C}^{*}}$-algebra by using states. Finally we utilize the linking algebra to give some equivalent assertions regarding parallel elements in a Hilbert ${{C}^{*}}$-module.

Keywords

47A3046L0546L0847B4715A60C*-algebraapproximate parallelismoperator parallelismHilbert C*-module

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 58 , Issue 1 , 01 March 2015 , pp. 207 - 224
Copyright
Copyright © Canadian Mathematical Society 2015

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