Journal article

Vector measures of bounded semivariation and associated convolution operators


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Author list: Mangatiana A. Robdera and Paulette Saab

Publisher: Cambridge University Press

Publication year: 2010

Journal: Glasgow Mathematical Journal

Journal acronym: GMJ

Volume number: 53

Issue number: 2

Start page: 333

End page: 340

Number of pages: 8

ISSN: 0017-0895

eISSN: 1469-509X

URL: https://www.cambridge.org/core/journals/glasgow-mathematical-journal/article/vector-measures-of-bounded-semivariation-and-associated-convolution-operators/7240A20C3DDC849CFCB97E3F6A113D40



Let G be a compact metrizable abelian group, and let X be a Banach space. We characterize convolution operators associated with a regular Borel X-valued measure of bounded semivariation that are compact (resp; weakly compact) from L1(G), the space of integrable functions on G into L1(G) X, the injective tensor product of L1(G) and X. Along the way we prove a Fourier Convergence theorem for vector measures of relatively compact range that are absolutely continuous with respect to the Haar measure.

Keywords: 46G10, 46B99


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Last updated on 2024-17-09 at 09:52