Polynomials on Banach lattices and positive tensor products. (English) Zbl 1245.46035
Authors’ abstract: This paper is the first systematic study of homogeneous polynomials on Banach lattices. A variety of new Banach spaces and Banach lattices of multilinear maps, homogeneous polynomials, and operators are introduced. The main technique is to employ positive tensor products and quotients of positive tensor products. Our theorems generalize the results on orthogonally additive polynomials by Y. Benyamini, S. Lassalle and J. G. Llavona [Bull. Lond. Math. Soc. 38, No. 3, 459–469 (2006; Zbl 1110.46033)], the results by B. C. Grecu and R. A. Ryan [Proc. Am. Math. Soc. 133, No. 4, 1083–1091 (2005; Zbl 1064.46028)], and the results by K. Sundaresan [DIMACS, Ser. Discrete
Math. Theor. Comput. Sci. 4, 571–586 (1991; Zbl 0745.46028)].
Reviewer: Mohamed Ali Toumi (Bizerte)
MSC:
| 46G25 | (Spaces of) multilinear mappings, polynomials |
| 46M05 | Tensor products in functional analysis |
| 47B65 | Positive linear operators and order-bounded operators |
| 46B42 | Banach lattices |
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