Multis

Klaus Deimling
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Klaus Deimling: Gesamthochschule Paderborn

Chapter Chapter 8 in Nonlinear Functional Analysis, 1985, pp 278-318 from Springer

Abstract: Abstract The multis considered in this chapter are harmless compared with their namesakes in daily life, since they are just multivalued maps, also called set-valued or multiple-valued maps. You meet them at an early stage as inverses of maps which are not one-to-one, though the multivalued aspect is usually suppressed in elementary courses. Think of complex function theory, where you just choose one branch of the logarithm or the n-th root for practical purposes before, perhaps, you study analytic continuation, or think of linear operator theory, where you just factor out the kernel of T∈L(X, Y) so that you have a nice inverse $${\hat T^{ - 1}}:R\left( T \right) \to X/N\left( T \right)$$ as in the proof of Proposition 7.9, or, since three is lucky, think of elementary differentiability where you either have a unique tangent (plane) or ‘nothing’.

Keywords: Banach Space; Compact Convex; Maximal Monotone; Real Banach Space; Continuous Selection (search for similar items in EconPapers)
Date: 1985
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DOI: 10.1007/978-3-662-00547-7_8

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