Jordan Triple Product Homomorphisms on Triangular Matrices to and from Dimension One
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Published:2018-05-16
Issue:
Volume:33
Page:147-159
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ISSN:1081-3810
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Container-title:The Electronic Journal of Linear Algebra
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language:
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Short-container-title:ELA
Author:
Kokol Bukovsek Damjana,Mojskerc Blaz
Abstract
A map $\Phi$ is a Jordan triple product (JTP for short) homomorphism whenever $\Phi(A B A)= \Phi(A) \Phi(B) \Phi(A)$ for all $A,B$. We study JTP homomorphisms on the set of upper triangular matrices $\mathcal{T}_n(\mathbb{F})$, where $\Ff$ is the field of real or complex numbers. We characterize JTP homomorphisms $\Phi: \mathcal{T}_n(\mathbb{C}) \to \mathbb{C}$ and JTP homomorphisms $\Phi: \mathbb{F} \to \mathcal{T}_n(\mathbb{F})$. In the latter case we consider continuous maps and the implications of omitting the assumption of continuity.
Publisher
University of Wyoming Libraries
Subject
Algebra and Number Theory
Cited by
1 articles.
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1. Jordan triple homomorphisms on $${\mathcal {T}}_\infty (F)$$;Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry;2021-08-02