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Autumn 2019 A trick for investigation of near-martingales in quantum probability spaces
Ghadir Sadeghi, Ali Talebi
Adv. Oper. Theory 4(4): 784-792 (Autumn 2019). DOI: 10.15352/aot.1903-1484

Abstract

‎‎‎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.

Citation

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Ghadir Sadeghi. Ali Talebi. "A trick for investigation of near-martingales in quantum probability spaces." Adv. Oper. Theory 4 (4) 784 - 792, Autumn 2019. https://doi.org/10.15352/aot.1903-1484

Information

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

zbMATH: 07064105
MathSciNet: MR3949975
Digital Object Identifier: 10.15352/aot.1903-1484

Subjects:
Primary: 46L53
Secondary: 46L10, 47A30, 60E15

Rights: Copyright © 2019 Tusi Mathematical Research Group

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Vol.4 • No. 4 • Autumn 2019
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