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IMA Journal of Mathematical Control and Information 1997 14(2):109-136; doi:10.1093/imamci/14.2.109
© 1997 by Institute of Mathematics and its Applications
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Vector-valued integration with applications to the operator-valued H{infty} space

E. G. F. THOMAS

Department of Mathematics, University of Groningen Postbus 800, 9700 AV Groningen, Holland

We generalize the Bochner integral by weakening the measurability assumption, while maintaining the integrability of the norm. For operator-valued functions this leads to the notion of strongly integrable operator-valued function, which is shown to be appropriate for the description of translation-invariant operators in spaces of vector-valued functions and in connection with the operator-valued analogue of the classical H{infty} space. The paper is expository.


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