Israel Journal of Mathematics

, Volume 72, Issue 3, pp 257–279 | Cite as

Smooth Banach spaces, weak asplund spaces and monotone or usco mappings

  • David Preiss
  • R. R. Phelps
  • I. Namioka


It is shown that if a real Banach spaceE admits an equivalent Gateaux differentiable norm, then for every continuous convex functionf onE there exists a denseG δ subset ofE at every point of whichf is Gateaux differentiable. More generally, for any maximal monotone operatorT on such a space, there exists a denseG δ subset (in the interior of its essential domain) at every point of whichT is single-valued. The same techniques yield results about stronger forms of differentiability and about generically continuous selections for certain upper-semicontinuous compact-set-valued maps.


Banach Space Monotone Operator Hausdorff Space Maximal Monotone Operator Winning Strategy 
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Copyright information

© Hebrew University 1990

Authors and Affiliations

  • David Preiss
    • 1
  • R. R. Phelps
    • 2
  • I. Namioka
    • 2
  1. 1.Department of MathematicsUniversity College LondonLondonUK
  2. 2.Mathematics Department GN-50University of WashingtonSeattleUSA

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