Lorenz, Klaus Jürgen An implicit function theorem in locally convex spaces. (English) Zbl 0562.46027 Math. Nachr. 129, 91-101 (1986). 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. Cited in 2 Documents MSC: 46G05 Derivatives of functions in infinite-dimensional spaces 58C15 Implicit function theorems; global Newton methods on manifolds 47L10 Algebras of operators on Banach spaces and other topological linear spaces 46A08 Barrelled spaces, bornological spaces Keywords:strict differentiability; locally convex spaces; bornological operator ideal of bounded operators; chain rule; implicit function theorem PDFBibTeX XMLCite \textit{K. J. Lorenz}, Math. Nachr. 129, 91--101 (1986; Zbl 0562.46027) Full Text: DOI References: [1] [Russian Text Ignored]. 23 pp 67– (1968) [2] Variétés différentielles et analytiques. Fascicule de résultats, [Russian Text Ignored]. 1–7, Hermann, Paris (1967) [3] Differential calculus, Hermann/Kershaw, Paris/London (1971) [4] Foundations of modern analysis, Academic Press, New York/London (1969) [5] Hogbe-Nlend, Springer Lecture Notes in Math. 331 pp 84– (1973) [6] Locally convex spaces and operator ideals, Teubner, Leipzig (1983) · Zbl 0552.46005 [7] Real analysis, second edition, Addison-Wesley, Reading/Mass. (1983) [8] Yamamuro, Springer Lecture Notes in Math. 374 (1974) · Zbl 0276.58001 · doi:10.1007/BFb0061580 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.