When A and B are closed subspace of a Hubert space X, and PA, PB are the corresponding orthogonal projections, von Neumann showed that
$${\left\lfloor {\left( {I - {P_A}} \right)\left( {I - {P_B}} \right)} \right\rfloor ^n}(x) \to (I - \frac{P}{{A + B}})(x){\kern 1pt} (x \in X)$$

This result is extended by replacing X with any smooth and uniformly convex Banach space, and A and B any closed subspaces whose corresponding metric projections PA, PB are linear. Further, it is shown that (a) holds whenever X is a uniformly smooth and uniformly convex Banach space and A, B closed subspaces such that A + B is closed.


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Copyright information

© Springer Basel AG 1979

Authors and Affiliations

  • Frank Deutsch
    • 1
    • 2
  1. 1.Pachbereich MathematikJ.W. Goethe UniversitätFrankfurt am MainGermany
  2. 2.Department of MathematicsThe Pennsylvania State UniversityUniversity ParkUSA

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