Abstract

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 YY of a Banach space XX, we show that if YY is constrained in a weakly compactly generated dual space, then the space L1(μ,Y)L^1(\mu,Y) of YY-valued Bochner integrable functions is coproximinal in L1(μ,X)L^1(\mu,X). This extends a result of M. R. Haddadi, N. Hejazjpoor and H. Mazaheri [Some results about best coapproximation in LP(S,X)L^P(S,X), Anal. Theory Appl. 26 (2010) 69–75], proved when YY is reflexive.

Author information

Contact details are reproduced from the original publication and may be historical.

T. S. S. R. K. Rao

Theoretical Statistics and Mathematics Division, Indian Statistical Institute, R. V. College P.O., Bangalore 560059, India

tss@isibang.ac.in

Keywords

  • Coproximinality
  • constrained subspaces
  • weakly compactly generated spaces
  • spaces of Bochner integrable functions
  • von Neumann's selection theorem

Mathematics Subject Classification

41A50; 46B20, 46E40

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Suggested citation

T. S. S. R. K. Rao. “Coproximinality in Spaces of Bochner Integrable Functions.” Journal of Convex Analysis 24 (2017), No. 3, 955–958. https://doi.org/10.68381/jca24056

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Published by Heldermann Verlag, 2017. Rights now held by Banach Press LLC.