## Bulletin of the Belgian Mathematical Society - Simon Stevin

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

### On the mathematical work of Jean Schmets

Klaus D. Bierstedt and José Bonet

#### 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