Document Type : Research Paper
Department of Mathematics and Applications, University of Mohaghegh Ardabili, Ardabi, Iran.
Department of Mathematics , University of Urmia, Urmia, Iran.
Let f : X × Y × Z → W be a bounded tri-linear map on normed spaces. We say that f is close-to-regular when ft∗∗∗∗s = fs∗∗∗∗t and we say that f is Aron-Berner regular when all natural extensions are equal. In this manuscript, we give a simple criterion for the close-to-regularity of tri-linear maps.