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An Implicit Function Theorem in Locally Convex Spaces
Author(s) -
Lorenz Klaus Jürgen
Publication year - 1986
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19861290108
Subject(s) - mathematics , banach space , locally convex topological vector space , pure mathematics , differentiable function , norm (philosophy) , bounded inverse theorem , eberlein–šmulian theorem , approximation property , lp space , discrete mathematics , bounded operator , topological space , political science , law
The notion of strict differentiability in BANACH spaces is generalized to locally convex spaces in such a way, that computations in the bornological operator ideal of bounded operators play the role of norm estimations. We get a remarkably rich theory including not only the easy formulas like the chain rule, but also the deep theorems like the implicit function theorem. The BANACH space proofs can be translated almost literally.