Regularity of bounded tri-linear maps and the fourth adjiont of a tri-derivation

In this Article, we give a simple criterion for the regularity of a tri-linear mapping. We provide if \(f:X\times Y\times Z\longrightarrow W \) is a bounded tri-linear mapping and \(h:W\longrightarrow S\) is a bounded linear mapping, then \(f\) is regular if and only if \(hof\) is regular. We also s...

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Bibliographic Details
Published in:arXiv.org 2019-11
Main Authors: Abotaleb Sheikhali, Ebadian, Ali, Azar, Kazem Haghnejad
Format: Article
Language:English
Subjects:
Derivation
Mapping
Regularity
Online Access:Get full text
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Summary:In this Article, we give a simple criterion for the regularity of a tri-linear mapping. We provide if \(f:X\times Y\times Z\longrightarrow W \) is a bounded tri-linear mapping and \(h:W\longrightarrow S\) is a bounded linear mapping, then \(f\) is regular if and only if \(hof\) is regular. We also shall give some necessary and sufficient conditions such that the fourth adjoint \(D^{***}\) of a tri-derivation \(D\) is again tri-derivation.
ISSN:2331-8422