Bulletin de la Société Royale des Sciences de Liège

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José BONET & Werner J. RICKER

SPECTRAL MEASURES IN CLASSES OF FRÉCHET SPACES

(Volume 73 - Année 2004 — Numéro 2 - 3)
Article
Open Access
Mots-clés : spectral measures, Köthe echelon space, vector measure, Radon-Nikodym property, Fréchet space, integrable function

Abstract

A detailed investigation is made of the canonical atomic spectral measure defined in such Fréchet spaces as the Köthe echelon sequence spaces and the sequence spaces , as well as the (non-atomic) "natural" spectral measures in such Fréchet spaces of measurable functions as the space of locally power integrable functions on and on [0,1].  Of particular interest are questions concerned with the range of the spectral measure, whether or not it has finite variation (for certain operator topologies), the Radon-Nikodým property of the underlying spaces involved and, most importantly, does the spectral measure admit unbounded integrable functions ?

To cite this article

José BONET & Werner J. RICKER, «SPECTRAL MEASURES IN CLASSES OF FRÉCHET SPACES», Bulletin de la Société Royale des Sciences de Liège [En ligne], Volume 73 - Année 2004, Numéro 2 - 3, 99 - 117 URL : http://popups.ulg.be/0037-9565/index.php?id=761.

About: José BONET

ETS Arquitectura, Departamento de Matemática Aplicada, Universidad Politécnia de Valencia, E-46071 Valencia (Spain), jbonet@mat.upv.es

About: Werner J. RICKER

Math.-Geogr. Fakultät, Katholische Universität, Eichstätt-Ingolstadt, D-85071 Eichstätt (Germany), werner.ricker@ku-eichstaett.de