The Schwartz property and nuclearity of spaces of smooth and holomorphic functions in infinite dimensions

DOI10.1017/S030500410006864XzbMath0707.46030MaRDI QIDQ3488716

Sten Bjon

Publication date: 1990

Published in: Mathematical Proceedings of the Cambridge Philosophical Society (Search for Journal in Brave)

zbMATH Keywords

continuous convergence\(L_ c\)-embeddedequable convergence structurelocally convex convergence spaceSchwartz property and nuclearity of spaces of smooth and holomorphic functions in infinite dimensions

Mathematics Subject Classification ID

Spaces of vector- and operator-valued functions (46E40) Infinite-dimensional holomorphy (46G20) Convergence in general topology (sequences, filters, limits, convergence spaces, nets, etc.) (54A20) Spaces determined by compactness or summability properties (nuclear spaces, Schwartz spaces, Montel spaces, etc.) (46A11) Other ``topological linear spaces (convergence spaces, ranked spaces, spaces with a metric taking values in an ordered structure more general than (mathbb{R}), etc.) (46A19) Spaces of differentiable or holomorphic functions on infinite-dimensional spaces (46E50) Rings and algebras of continuous, differentiable or analytic functions (46E25) Tensor products in functional analysis (46M05)

Cites Work

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• Zur Theorie der Schwartz-Räume
• Limesräume
• A general approach to infinite-dimensional holomorphy
• Continuous convergence on C(X)
• An example of a nuclear space in infinite dimensional holomorphy
• Marinescu-Räume
• The Approximation Property for Nuclear Convergence Vector Spaces
• Characterization of Schwartz Spaces by their Holomorphic Duals
• Einbettbarkeit in den Bidualraum und Darstellbarkeit als projektiver Limes in Kategorien von Limesvektorräumen
• Differentation under the integral sign and holomorphy.

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