Advances in Operator Theory

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

Ghadir Sadeghi and Ali Talebi

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‎‎‎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.

Article information

Adv. Oper. Theory, Volume 4, Number 4 (2019), 784-792.

Received: 18 February 2019
Accepted: 1 April 2019
First available in Project Euclid: 15 May 2019

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 46L53: Noncommutative probability and statistics
Secondary: 46L10‎ ‎60E15‎ ‎47A30

quantum probability space Gundy decomposition‎ noncommutative near-martingale Doob decomposition Riesz decomposition


Sadeghi, Ghadir; Talebi, Ali. A trick for investigation of near-martingales in quantum probability spaces. Adv. Oper. Theory 4 (2019), no. 4, 784--792. doi:10.15352/aot.1903-1484.

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