Research PaperNo Access

Some results for a class of extended centralizers on $C^{*}$ -algebras

Anamika Sarma

Department of Mathematics, Gauhati University, Assam, India

E-mail Address: sarma.anamika53@gmail.com

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Nilakshi Goswami

Department of Mathematics, Gauhati University, Assam, India

E-mail Address: nila_g2003@yahoo.co.in

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, and

Vishnu Narayan Mishra

https://orcid.org/0000-0002-2159-7710

Department of Mathematics, Indira Gandhi National Tribal University, Lalpur, Amarkantak, Anuppur, Madhya Pradesh 484887, India

E-mail Address: vishnunarayanmishra@gmail.com

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https://doi.org/10.1142/S1793830920500871Cited by:1 (Source: Crossref)

Abstract

The aim of this paper is to introduce a new class of generalized centralizers on $C^{*}$ -algebras which is termed as extended $(k_{1}, k_{2})$ -centralizer. We study different properties of this class of centralizers. Moreover, we define a class of $C^{*}$ -algebras which contains the prime $C^{*}$ -algebras as a subclass. Different properties of extended centralizers with respect to this class of $C^{*}$ -algebras are discussed with suitable examples.

Keywords:

AMSC: 46L06, 22D25, 47B47

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