Bulletin of the Belgian Mathematical Society - Simon Stevin

On the mathematical work of Jean Schmets

Klaus D. Bierstedt and José Bonet

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Abstract

In the introductory Section 0. some of the most important points in the professional curriculum vitae of Jean Schmets are given. Then Section 1 is devoted to present (part of) the work for which Schmets was very well known until 1990: He has been the leading specialist in the world for locally convex spaces $C(X)$ of continuous functions with various topologies and for the corresponding spaces $C(X,E)$ of vector valued continuous functions. Finally, in Section 2 some results which Schmets obtained in cooperation with Manuel Valdivia since 1990 are reviewed: work on domains of real analytic existence, continuous linear right inverses for $C^\infty$- functions and Whitney extensions for non quasianalytic functions.

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 14, Number 3 (2007), 385-405.

Dates
First available in Project Euclid: 28 September 2007

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1190994201

Digital Object Identifier
doi:10.36045/bbms/1190994201

Mathematical Reviews number (MathSciNet)
MR2387037

Zentralblatt MATH identifier
1161.01019

Subjects
Primary: 01A70
Secondary: 26E05: Real-analytic functions [See also 32B05, 32C05] 26E10: $C^\infty$-functions, quasi-analytic functions [See also 58C25] 46A08: Barrelled spaces, bornological spaces 46A63: Topological invariants ((DN), ($\Omega$), etc.) 46E10: Topological linear spaces of continuous, differentiable or analytic functions 46E25: Rings and algebras of continuous, differentiable or analytic functions {For Banach function algebras, see 46J10, 46J15} 46E40: Spaces of vector- and operator-valued functions 46G20: Infinite-dimensional holomorphy [See also 32-XX, 46E50, 46T25, 58B12, 58C10] 46M18: Homological methods (exact sequences, right inverses, lifting, etc.)

Keywords
spaces of (vector valued) continuous functions (quasi)barrelled and (ultra)bornological spaces associated with a locally convex space domains of real analytic existence Borel theorem Whitney jets continuous linear right inverses for restriction maps Whitney extensions for non quasianalytic functions real analytic extensions

Citation

Bierstedt, Klaus D.; Bonet, José. On the mathematical work of Jean Schmets. Bull. Belg. Math. Soc. Simon Stevin 14 (2007), no. 3, 385--405. doi:10.36045/bbms/1190994201. https://projecteuclid.org/euclid.bbms/1190994201


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