The Borel theorem for infinitely differentiable functions from a normed space into a Banach space

zbMATH Open0891.46016MaRDI QIDQ1363850

Yakov Valentinovich Radyno, S. A. Tuzik

Publication date: 20 August 1997

Published in: Doklady Mathematics (Search for Journal in Brave)

zbMATH Keywords

Fréchet derivativesurjectivityFréchet spacesurjectivity theoremBorel theoremB-complete space\(C^ \infty\)-functions between normed spacesfully complete spaceMittag-Leffler type theoremPták spacesymmetric \(k\)-linear mappings

Mathematics Subject Classification ID

Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product) (46C05) Spaces of vector- and operator-valued functions (46E40) Infinite-dimensional holomorphy (46G20) Spaces of operators; tensor products; approximation properties (46B28) Topological linear spaces of continuous, differentiable or analytic functions (46E10) Locally convex Fréchet spaces and (DF)-spaces (46A04) Spaces of linear operators; topological tensor products; approximation properties (46A32) Open mapping and closed graph theorems; completeness (including (B)-, (B_r)-completeness) (46A30) Spaces of differentiable or holomorphic functions on infinite-dimensional spaces (46E50)

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