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February 2021 Maps preserving strong products
Ensiyeh Tavakoli, Ali Taghavi
Rocky Mountain J. Math. 51(1): 315-325 (February 2021). DOI: 10.1216/rmj.2021.51.315

Abstract

Let 𝒜 be an arbitrary C-algebra which contains a nontrivial projection P1 and let φ:𝒜𝒜 be a surjective map which satisfies

φ(A1)ηφ(A2)ηηφ(An1)ηφ(P)=A1ηA2ηηAn1ηP

for every A1,A2,,An1𝒜 (n3), P{P1,IP1}, and some ηC, such that |η|=1, η±1, and A1ηA2ηηAn1ηP is the Jordan multiple η--product where A1ηA2=A1A2+ηA2A1. We determine the concrete form of map φ on any arbitrary C-algebra. Also, if n3, η=1 and 𝒜 is an arbitrary -algebra (with unit I), over the complex field C which contains a nontrivial projection P1, then φ is of the form φ(T)=Tφ(I) for all T𝒜.

Citation

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Ensiyeh Tavakoli. Ali Taghavi. "Maps preserving strong products." Rocky Mountain J. Math. 51 (1) 315 - 325, February 2021. https://doi.org/10.1216/rmj.2021.51.315

Information

Received: 16 February 2020; Revised: 16 August 2020; Accepted: 21 August 2020; Published: February 2021
First available in Project Euclid: 28 May 2021

Digital Object Identifier: 10.1216/rmj.2021.51.315

Subjects:
Primary: 46J10 , 46L10 , 47B48

Keywords: preserving maps , strong products

Rights: Copyright © 2021 Rocky Mountain Mathematics Consortium

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Vol.51 • No. 1 • February 2021
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