Tensor product representation of Köthe-Bochner spaces and their dual spaces

Tensor product representation of Köthe-Bochner spaces and their dual spaces We provide a tensor product representation of Köthe-Bochner function spaces of vector valued integrable functions. As an application, we show that the dual space of a Köthe-Bochner function space can be understood as a space of operators satisfying a certain extension property. We apply our results in order to give an alternate representation of the dual of the Bochner spaces of p-integrable functions and to analyze some properties of the natural norms $$\Delta _p$$ Δ p that are defined on the associated tensor products. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

Tensor product representation of Köthe-Bochner spaces and their dual spaces

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Publisher
Springer Journals
Copyright
Copyright © 2015 by Springer Basel
Subject
Mathematics; Fourier Analysis; Operator Theory; Potential Theory; Calculus of Variations and Optimal Control; Optimization; Econometrics
ISSN
1385-1292
eISSN
1572-9281
D.O.I.
10.1007/s11117-015-0347-3
Publisher site
See Article on Publisher Site

Abstract

We provide a tensor product representation of Köthe-Bochner function spaces of vector valued integrable functions. As an application, we show that the dual space of a Köthe-Bochner function space can be understood as a space of operators satisfying a certain extension property. We apply our results in order to give an alternate representation of the dual of the Bochner spaces of p-integrable functions and to analyze some properties of the natural norms $$\Delta _p$$ Δ p that are defined on the associated tensor products.

Journal

PositivitySpringer Journals

Published: Jul 2, 2015

References

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