Pseudocomplémentation dans les espaces de Banach

Patric Rauch

Studia Mathematica (1991)

  • Volume: 100, Issue: 3, page 251-282
  • ISSN: 0039-3223


This paper introduces the following definition: a closed subspace Z of a Banach space E is pseudocomplemented in E if for every linear continuous operator u from Z to Z there is a linear continuous extension ū of u from E to E. For instance, every subspace complemented in E is pseudocomplemented in E. First, the pseudocomplemented hilbertian subspaces of L ¹ are characterized and, in L p with p in [1, + ∞[, classes of closed subspaces in which the notions of complementation and pseudocomplementation are equivalent are pointed out. Then, for Banach spaces with the uniform approximation property, Dvoretzky’s theorem is strengthened by proving that they contain uniformly pseudocomplemented n 2 ’s. Finally, the study of Banach spaces in which every closed subspace is pseudocomplemented is started.

How to cite


Rauch, Patric. "Pseudocomplémentation dans les espaces de Banach." Studia Mathematica 100.3 (1991): 251-282. <>.

author = {Rauch, Patric},
journal = {Studia Mathematica},
keywords = {pseudocomplemented subspaces in a Banach space; constant of pseudocomplementedness; independent stochastic Gaussian variables; theorem of Dvoretzky type; spaces with uniform approximation property},
language = {fre},
number = {3},
pages = {251-282},
title = {Pseudocomplémentation dans les espaces de Banach},
url = {},
volume = {100},
year = {1991},

AU - Rauch, Patric
TI - Pseudocomplémentation dans les espaces de Banach
JO - Studia Mathematica
PY - 1991
VL - 100
IS - 3
SP - 251
EP - 282
LA - fre
KW - pseudocomplemented subspaces in a Banach space; constant of pseudocomplementedness; independent stochastic Gaussian variables; theorem of Dvoretzky type; spaces with uniform approximation property
UR -
ER -


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