Coproximinality in spaces of Bochner integrable functions

Article Type

Research Article

Publication Title

Journal of Convex Analysis


In this short note we use a new way of applying von Neumann's selection theorem for obtaining best coapproximation in spaces of measurable functions. For a coproximinal closed subspace Y of a Banach space X, we show that if Y is constrained in a weakly compactly generated dual space, then the space L1 (μ, Y ) of Y-valued Bochner integrable functions is coproximinal in L1 (μ, X). This extends a result of Haddadi et. al., proved when Y is reflexive.

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