IJPAM: Volume 110, No. 2 (2016)

Title

LEFT IDEALS PRESERVING LINEAR MAPS
BETWEEN $C^*$-ALGEBRAS

Authors

Rohollah Parvinianzadeh$^1$, Ali Taghavi$^2$
$^1$Department of Mathematics
University of Yasouj
P.O. Box 75918-74831, Yasouj, IRAN
$^2$Department of Mathematics
Faculty of Mathematical Sciences
University of Mazandaran
P.O. Box 47416-1468, Babolsar, IRAN

Abstract

In this paper we show that if $A$ is a unital $C^{*}$-algebra and $B$ is a purely infinite $C^{*}$-algebra such that has a non-zero commutative maximal ideal and $\phi:A \rightarrow B$ is a unital surjective linear map which preserves the maximal left ideals in both direction. Then $\phi$ is a Jordan isomorphism.

History

Received: January 14, 2016
Revised: August 12, 2016
Published: November 5, 2016

AMS Classification, Key Words

AMS Subject Classification: 47D25, 47B49, 47A10
Key Words and Phrases: Banach algebra, $C^*$-algebra, Jordan homomorphism, left ideal, linear preserving, spectral isometry

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How to Cite?

DOI: 10.12732/ijpam.v110i2.1 How to cite this paper?

Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2016
Volume: 110
Issue: 2
Pages: 251 - 256


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