Applications of Hypocontinuous Bilinear Maps in Infinite-Dimensional Differential Calculus

Helge Glöckner ()
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Helge Glöckner: Universität Paderborn, Institut für Mathematik

Chapter 16 in Generalized Lie Theory in Mathematics, Physics and Beyond, 2009, pp 171-186 from Springer

Abstract: Paradigms of bilinear maps β: E >1 ×; E >2 → F between locally convex spaces (like evaluation or composition) are not continuous, but merely hypocon-tinuous. We describe situations where, nonetheless, compositions of β with Keller -maps (on suitable domains) are. Our main applications concern holomorphic families of operators, and the foundations of locally convex Poisson vector spaces.

Keywords: Open Subset; Topological Space; Compact Subset; Poisson Bracket; Topological Vector Space (search for similar items in EconPapers)
Date: 2009
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-540-85332-9_16

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DOI: 10.1007/978-3-540-85332-9_16

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