EMIS ELibM Electronic Journals Zeitschrift für Analysis und ihre Anwendungen
Vol. 18, No. 3, pp. 713-732 (1999)

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A Compactness Criterion of Mixed Krasnoselski{\u\i}-Riesz Type in Regular Ideal Spaces of Vector Functions

M. Väth

M. Väth: University of Würzburg, Department of Mathematics, Am Hubland, D-97074 Würz\-burg; \ e-mail: vaeth@cip.mathematik.uni-wuerzburg.de

Abstract: We present a compactness criterion in ideal spaces of vector-valued functions. In the case of real functions, the criterion gives a precise formula for the measure of non-compactness. In the Lebesgue-Bochner spaces $L_p(\R^n,U)$ the result can be interpreted as a Riesz compactness criterion and generalizes a theorem of Orlicz and Szufla.

Keywords: riesz compactness criterion, Krasnoselski{\u\i} compactness criterion, ideal spaces, K{ö}the spaces, Banach function spaces, spaces of measurable functions, vector-valued functions

Classification (MSC2000): 46E30, 46E40, 45N10, 46G10

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Electronic fulltext finalized on: 7 Aug 2001. This page was last modified: 9 Nov 2001.

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