Corpus ID: 231846932

The SHAI property for the operators on L^p

  title={The SHAI property for the operators on L^p},
  author={William B. Johnson and N. Christopher Phillips and Gideon Schechtman},
A Banach space X has the SHAI (surjective homomorphisms are injective) property provided that for every Banach space Y , every continuous surjective algebra homomorphism from the bounded linear operators on X onto the bounded linear operators on Y is injective. The main result gives a sufficient condition for X to have the SHAI property. The condition is satisfied for Lp(0, 1) for 1 < p < ∞, spaces with symmetric bases that have finite cotype, and the Schatten p-spaces for 1 < p < ∞. 1 The main… Expand
1 Citations
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On the subspaces of L (p > 2) spanned by sequences of independent random variables
  • Israel J. Math. 8
  • 1970
Examples of Lp spaces (1 < p 6= 2 < ∞)
  • Israel J. Math. 22
  • 1975
lczyński, The main triangle projection in matrix spaces and its applications
  • Studia Math
  • 1970