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arXiv · 1911.01038

Close-to-regularity and completely regularity of bounded tri-linear maps

Abotaleb Sheikhali·Ali Ebadian·Kazem Haghnejad Azar
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Abstract

Let $f:X\times Y\times Z\longrightarrow W $ be a bounded tri-linear map on normed spaces. We say that $f$ is close-to-regular when $f^{t****s}=f^{s****t}$ and we say that $f$ is completely regular when all natural extensions are equal. In this manuscript, we have some results on the close-to-regular maps and investigate the close-to-regularity of tri-linear maps. We investigate the relation between Arens regularity of bounded bilinear maps and close-to-regularity bounded tri-linear maps. We give a simple criterion for the completely regularity of tri-linear maps. We provide a necessary and sufficient condition such that the fourth adjoint $D^{****}$ of a tri-derivation is again a tri-derivation.

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Abotaleb Sheikhali, Ali Ebadian, Kazem Haghnejad Azar. 2019-11-04. Close-to-regularity and completely regularity of bounded tri-linear maps. https://arxiv.org/abs/1911.01038

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