Applications of hypocontinuous bilinear maps in infinite-dimensional differential calculus

2007/01/02 by Helge Glockner, Glockner, Helge
Mathematics · Physics and Astronomy · #22E65 #26E15 #26E20 (primary) 17B63 #46A32 #46G20 #46T25 (secondary) #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Mathematical Physics (math-ph) #math-ph #math.FA #math.MP #msc:17B63 #msc:22E65 #msc:26E15 #msc:26E20 #msc:46A32 #msc:46G20 #msc:46T25

paper · pdf · doi:10.48550/arxiv.math/0701072

21 pages, LaTeX (v2: discussion of non-reflexive Poisson vector spaces and further material added; extended preprint version)

arxiv created 2007/01/14 · arxiv updated 2009/12/01

Abstract

Paradigms of bilinear maps f between locally convex spaces (like evaluation or composition) are not continuous, but merely hypocontinuous. We describe situations where, nonetheless, compositions of f with Keller Cⁿ_c-maps (on suitable domains) are Cⁿ_c. Our main applications concern holomorphic families of operators, and the foundations of locally convex Poisson vector spaces.

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