Compactness of the integration operator associated with a vector measure

• Autorzy: S. Okada , W. J. Ricker , L. Rodríguez-Piazza
• Języki publikacji: EN

Abstrakty

EN

A characterization is given of those Banach-space-valued vector measures m with finite variation whose associated integration operator Iₘ: f ↦ ∫fdm is compact as a linear map from L¹(m) into the Banach space. Moreover, in every infinite-dimensional Banach space there exist nontrivial vector measures m (with finite variation) such that Iₘ is compact, and other m (still with finite variation) such that Iₘ is not compact. If m has infinite variation, then Iₘ is never compact.

Kategorie tematyczne

• 28B05: Vector-valued set functions, measures and integrals
• 46G10: Vector-valued measures and integration

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2002
• Tom: 150
• Numer: 2
• Strony: 133-149

Daty

wydano

2002

Twórcy

autor

S. Okada

• School of Mathematics, The University of New South Wales, Sydney, NSW 2052, Australia
• Department of Mathematics, Macquarie University, Sydney, NSW 2109, Australia

autor

W. J. Ricker

• School of Mathematics, The University of New South Wales, Sydney, NSW 2052, Australia
• Math.-Geogr. Fakutät, Katholitsche Universität Eichstätt, D-85071 Eichstätt, Germany

autor

L. Rodríguez-Piazza

• Departamento de Anáisis Matemático, Facultad de Matemáticas, Universidad de Sevilla, Aptdo. 1160, 41080 Sevilla, Spain

Identyfikatory

DOI

10.4064/sm150-2-3