Abstract
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.
-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 language | English |
|---|---|
| Pages (from-to) | 4079-4110 |
| Journal | Transactions of the American Mathematical Society |
| Volume | 367 |
| Issue number | 6 |
| DOIs | |
| Publication status | Published - 1 Jun 2015 |
| Externally published | Yes |
Keywords
- Boyd interpolation theorem
- noncommutative symmetric spaces
- -moment inequalities
- Doob maximal inequality
- Burkholder-Davis-Gundy inequalities
- Burkholder-Rosenthal inequalities