## Non-commutative martingale inequalities

### Abstract

We prove the analogue of the classical Burkholder-Gundy inequalites for non-commutative martingales. As applications we give a characterization for an Ito-Clifford integral to be an $L^p$-martingale via its integrand, and then extend the Ito-Clifford integral theory in $L^2$, developed by Barnett, Streater and Wilde, to $L^p$ for all $1<p<\infty$. We include an appendix on the non-commutative analogue of the classical Fefferman duality between $H^1$ and $BMO$

Topics: Mathematics - Functional Analysis, 46L50
Publisher: 'Springer Science and Business Media LLC'
Year: 1997
DOI identifier: 10.1007/s002200050224
OAI identifier: oai:arXiv.org:math/9704209

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