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and interpolation between Banach lattices

Authors:	Nahum Zobin Veronica Zobin

Institution:	Department of Mathematics and Computer Science, University of Miami, Coral Gables, Florida 33124 ; Department of Mathematics, Technion -- I.I.T., Haifa, 32000, Israel

Abstract:	We study the possibility of obtaining the $l_{\infty }$ -norm by an interpolation method starting from a couple of Banach lattice norms. We describe all couples of Banach lattice norms in ${\mathbb {R}}^{n}$ such that the $l_{\infty }$ -norm is a strict interpolation norm between them. Further we consider the possibility of obtaining the $l_{\infty }$ -norm by any method which guarantees interpolation of not only linear operators (= bilinear forms on ${\mathbb {R}}^{n}\times {\mathbb {R}}^{n})$ but also of all polylinear forms. Here we show that either one of the initial norms has to be proportional to the $l_{\infty }$ -norm, or both have to be weighted $l_{\infty }$ -norms.

Keywords:	Banach lattices interpolation of operators complex method

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