L^p-spaces with respect to conditional expectation on Riesz spaces

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• 作者：Youssef Azouzi ; ^{youssef.azouzi@ipest.rnu.tn" class="auth_mail" title="E-mail the corresponding author} ; Mejdi Trabelsi ^{trab.majdi@gmail.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Vector lattice ; F-Algebra ; Conditional expectation ; Functional calculus ; Inequalities
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2017
• 出版时间：15 March 2017
• 年：2017
• 卷：447
• 期：2
• 页码：798-816
• 全文大小：398 K

文摘

Recently, Labuschagne and Watson introduced the space L²(T)$L^2\left(T\right)$ for a conditional expectation T   with natural domain a Riesz space L¹(T)$L^1\left(T\right)$. The main purpose of this paper is to carry on with this process by introducing and investigate the spaces L^p(T)$L^p\left(T\right)$ with p∈[1,∞]$p\in [1,\infty ]$.