A trick for investigation of near-martingales in quantum probability spaces

Document Type: Original Article

Authors

1 ‎Hakim Sabzevari University‎, Iran

2 ‎Ferdowsi University of Mashhad‎, Iran

Abstract

‎‎In this paper‎, ‎we introduce near-martingales in the setting of quantum probability spaces and present a trick for investigating some of their properties‎. ‎For instance‎, ‎we give a near-martingale analogous result of the fact that the space of all bounded $L^p$-martingales‎, ‎equipped with the norm $\|\cdot\|_p$‎, ‎is isometric to $L^p(\mathfrak{M})$ for $p>1$‎. ‎We also present Doob and Riesz decompositions for the near-submartingale and provide Gundy's decomposition for $L^1$-bounded near-martingales‎. ‎In addition‎, ‎the interrelation between near-martingales and the instantly independence is studied.

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