STRONG CONVERGENCE OF MARTINGALES IN VON NEUMANN ...

1 downloads 0 Views 430KB Size Report
11^11= sup |*(x)|= sup \i(e(x))\= ||t(^)||,. xEN. xeM l|x||
proceedings of the american mathematical

Volume 88. Number 3, July 1983

society



STRONG CONVERGENCEOF MARTINGALES IN VON NEUMANNALGEBRAS MAKOTO TSUKADA Abstract. In this paper we prove strong and ¿'-norm convergence of martingales with respect to a faithful normal semifinite weight on a von Neumann algebra.

1. Introduction. Let M be a von Neumann algebra and