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Some nicely placed Hardy spaces

Published online by Cambridge University Press:  01 March 1998

C. FINET  and
D. J. H. GARLING
C. FINET
Affiliation:
Institut de mathématique et d'informatique, Université de Mons-Hainaut, Mons, Belgium
D. J. H. GARLING
Affiliation:
St John's College, Cambridge
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Abstract

Let L0=L0(Ω, [sum ], μ) denote the vector space of (equivalence classes of) measurable functions on a measure space (Ω, [sum ], μ), taking values in a finite-dimensional Hilbert space H. We give L0 the topology τ0 of local convergence in measure[ratio ]τ0 is a complete vector space topology, with base of neighbourhoods

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where

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Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 123 , Issue 2 , March 1998 , pp. 329 - 335
Copyright
Cambridge Philosophical Society 1998

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