Bulletin of the Belgian Mathematical Society - Simon Stevin

Polynomial characterization of Asplund spaces

Raffaella Cilia and Joaquín Gutiérrez

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Abstract

We prove that, given an index $m$, if every Pietsch integral $m$-homo\-geneous polynomial on a Banach space $E$ is nuclear, then $E$ is Asplund. The converse was proved by Alencar.

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 12, Number 3 (2005), 393-400.

Dates
First available in Project Euclid: 8 September 2005

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1126195343

Digital Object Identifier
doi:10.36045/bbms/1126195343

Mathematical Reviews number (MathSciNet)
MR2173701

Zentralblatt MATH identifier
1114.46034

Subjects
Primary: 46G25
Secondary: 46B20: Geometry and structure of normed linear spaces 47H60: Multilinear and polynomial operators [See also 46G25]

Keywords
Pietsch integral polynomial nuclear polynomial

Citation

Cilia, Raffaella; Gutiérrez, Joaquín. Polynomial characterization of Asplund spaces. Bull. Belg. Math. Soc. Simon Stevin 12 (2005), no. 3, 393--400. doi:10.36045/bbms/1126195343. https://projecteuclid.org/euclid.bbms/1126195343


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