Spaces Snu, diametral dimension and property Omega bar

[en] This paper investigates two topological invariants in the context of the sequence spaces Snu, which are metric topological vector spaces defined in order to study the regularity of signals. First, it extends the formula already known of the diametral dimension of spaces Snu to some non-locally pseudoconvex ones. Second, it proves that locally p-convex spaces Snu verifies the property "Omega id", which is equivalent to Omega bar for Fréchet spaces.

Disciplines :

Mathematics

Author, co-author :

Demeulenaere, Loïc ; Université de Liège > Département de mathématique > Analyse - Analyse fonctionnelle - Ondelettes

Language :

English

Title :

Spaces Snu, diametral dimension and property Omega bar

Publication date :

2017

Journal title :

Journal of Mathematical Analysis and Applications

ISSN :

0022-247X

eISSN :

1096-0813

Publisher :

Academic Press, San Diego, United States - California

Volume :

449

Issue :

Pages :

1340-1350

Peer reviewed :

Peer Reviewed verified by ORBi

Funders :

FRIA - Fonds pour la Formation à la Recherche dans l'Industrie et dans l'Agriculture

Commentary :

Accepted for publication on December 22, 2016.

Available on ORBi :

since 23 December 2016

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Bibliography

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[11] Pietsch, A., Nuclear Locally Convex Spaces. Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 66, 1972, Springer-Verlag, Berlin translated from German by William H. Ruckle.
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[14] Vogt, D., Some results on continuous linear maps between Frechet spaces. Bierstedt, K.-D., Fuchssteiner, B., (eds.) North-Holland Mathematics Studies, vol. 90, 1984, 349–381.
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