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 × 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. 


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