Bulletin of the
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BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2023; 60(1): 137-148

Online first article July 8, 2022      Printed January 31, 2023

https://doi.org/10.4134/BKMS.b210939

Copyright © The Korean Mathematical Society.

Inductive limit in the category of $C^{\ast}$-ternary rings

Arpit Kansal, Ajay Kumar, Vandana Rajpal

University Of Delhi; University Of Delhi; Shivaji College

Abstract

We show the existence of inductive limit in the category of $C^{\ast}$-ternary rings. It is proved that the inductive limit of $C^{\ast}$-ternary rings commutes with the functor $\mathcal{A}$ in the sense that if $(M_n, \phi_n)$ is an inductive system of $C^{\ast}$-ternary rings, then $\varinjlim \mathcal{A}(M_n)=\mathcal{A}(\varinjlim M_n)$. Some local properties (such as nuclearity, exactness and simplicity) of inductive limit of $C^{\ast}$-ternary rings have been investigated. Finally we obtain $\varinjlim M_n^{\ast\ast}=(\varinjlim M_n)^{\ast\ast}$.

Keywords: Inductive limit, C$^*$-ternary rings, TRO, C$^*$-algebras

MSC numbers: 46L06, 46L07, 46M40

Supported by: The research of the first author is supported by the National Board of Higher Mathematics(NBHM), Government of India. The second author acknowledges support from National Academy of Sciences, India.

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