SPECTRAL MEASURES IN CLASSES OF FRÉCHET SPACES
ETS Arquitectura, Departamento de Matemática Aplicada, Universidad Politécnia de Valencia, E-46071 Valencia (Spain), jbonet@mat.upv.es
Math.-Geogr. Fakultät, Katholische Universität, Eichstätt-Ingolstadt, D-85071 Eichstätt (Germany), werner.ricker@ku-eichstaett.de
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 ?