Close-to-Regularity of Bounded Tri-Linear Maps

Document Type : Research Paper


1 Independent Researcher.

2 Department of Mathematics and Applications, University of Mohaghegh Ardabili, Ardabi, Iran.

3 Department of Mathematics , University of Urmia, Urmia, Iran.


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 Aron-Berner 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.