Noncommutative Boyd interpolation theorems

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We present a new, elementary proof of Boyd’s interpolation theorem. Our approach naturally yields a noncommutative version of this result and even allows for the interpolation of certain operators on
-valued noncommutative symmetric spaces. By duality we may interpolate several well-known noncommutative maximal inequalities. In particular we obtain a version of Doob’s maximal inequality and the dual Doob inequality for noncommutative symmetric spaces. We apply our results to prove the Burkholder-Davis-Gundy and Burkholder-Rosenthal inequalities for noncommutative martingales in these spaces.
Original languageEnglish
Pages (from-to)4079-4110
JournalTransactions of the American Mathematical Society
Issue number6
Publication statusPublished - 1 Jun 2015
Externally publishedYes


  • Boyd interpolation theorem
  • noncommutative symmetric spaces
  • -moment inequalities
  • Doob maximal inequality
  • Burkholder-Davis-Gundy inequalities
  • Burkholder-Rosenthal inequalities


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