A note on a selector theorem in Banach spaces

  • Jon K. Cole
Technical Note

Abstract

The existence of a strongly measurable function taking its values in a variable subset of a separable and reflexive Banach space was shown in Ref. 1. Here, we show the collection of all such functions to be weakly compact in itself.

Keywords

Banach Space Measurable Function Reflexive Banach Space Weakly Compact Variable Subset 

References

  1. 1.
    Cole, J. K.,A Selector Theorem in Banach Spaces, Journal of Optimization Theory and Applications, Vol. 7, No. 3, 1971.Google Scholar
  2. 2.
    Cesari, L.,Existence Theorems for Multidimensional Lagrange Problems, Journal of Optimization Theory and Applications, Vol. 1, No. 2, 1967.Google Scholar
  3. 3.
    Hille, E., andPhillips, R. S.,Functional Analysis and Semi-Groups, The Waverly Press, Baltimore, Maryland, 1957.Google Scholar
  4. 4.
    Dunford, N., andSchwartz, J.,Linear Operators, John Wiley and Sons (Interscience Publishers), New York, 1958.Google Scholar
  5. 5.
    Royden, H.,Real Analysis, The Macmillan Company, New York, 1968.Google Scholar

Copyright information

© Plenum Publishing Corporation 1972

Authors and Affiliations

  • Jon K. Cole
    • 1
  1. 1.Department of MathematicsSt. John's UniversityJamaica

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