Products and Factors of Banach function spaces

2008/03/30 by Anton R. Schep, Schep, Anton R.
Mathematics · #46E30 #47B38 #FOS: Mathematics #Functional Analysis (math.FA) #math.FA #msc:46E30 #msc:47B38

paper · pdf · doi:10.48550/arxiv.0803.4336

16 pages

arxiv created 2008/03/30 · arxiv updated 2009/12/01

Abstract

Given two Banach function spaces we study the pointwise product space E.F, especially for the case that the pointwise product of their unit balls is again convex. We then give conditions on when the pointwise product E . M(E, F)=F, where M(E,F) denotes the space of multiplication operators from E into F.

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• Pointwise products of some Banach function spaces and factorization
• Product spaces generated by bilinear maps and duality
• Multiplication of convex sets in C(K) spaces
• Boundedness of Functions on Product Spaces by Sums of Functions on the Factors
• Symmetrization, factorization and arithmetic of quasi-Banach function spaces