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The weak cotype 2 and the Orlicz property of the Lorentz sequence space d(a, 1)
Published online by Cambridge University Press: 18 May 2009
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The question “Does a Banach space with a symmetric basis and weak cotype 2 (or Orlicz) property have cotype 2?” is being seriously considered but is still open though the similar question for the r.i. function space on [0, 1] has an affirmative answer. (If X is a r.i. function space on [0, 1] and has weak cotype 2 (or Orlicz) property then it must have cotype 2.) In this note we prove that for Lorentz sequence spaces d(a, 1) they both hold.
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- Copyright © Glasgow Mathematical Journal Trust 1992
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