A CHARACTERIZATION OF HILBERT SPACES BY THE SUPREMUM VALUE OF SOME EXPECTATIONS

  • MOK JIN SIK (Department of Mathematics, Sun Moon University)
  • Published : 2005.01.01

Abstract

A Banach space X is a Hilbert space if and only if $$E{\mid}x=Y{\mid}{\le}2$$ for all x$\in$ X and all X-valued Bochner integrable functions Y satisfying EY = 0 and ${\mid}x-Y{\mid}{\le}2$ a.e.

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