Regularity of Bounded Tri-Linear Maps and the Fourth Adjoint of a Tri-Derivation

Document Type: Research Paper

Authors

1 payame noor univercity

2 Payame Noor Univercity

3 mohagheghe ardabili

10.22128/gadm.2020.358.1028

Abstract

In this Article, we give a simple criterion for the regularity of a tri-linear mapping. We provide if f : X × Y × Z −→ W is a bounded tri-linear mapping and h : W −→ 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.

Keywords