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 n id="mmlsi1" class="mathmlsrc">n class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X16305996&_mathId=si1.gif&_user=111111111&_pii=S0022247X16305996&_rdoc=1&_issn=0022247X&md5=951d858bdfa8433e01b512e4760b9ed4" title="Click to view the MathML source">L²(T)n>n class="mathContainer hidden">n class="mathCode">n>n>n> for a conditional expectation T   with natural domain a Riesz space n id="mmlsi16" class="mathmlsrc">n class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X16305996&_mathId=si16.gif&_user=111111111&_pii=S0022247X16305996&_rdoc=1&_issn=0022247X&md5=bcc3c2aae66b194f2e57de21bf033e25" title="Click to view the MathML source">L¹(T)n>n class="mathContainer hidden">n class="mathCode">n>n>n>. The main purpose of this paper is to carry on with this process by introducing and investigate the spaces n id="mmlsi24" class="mathmlsrc">n class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X16305996&_mathId=si24.gif&_user=111111111&_pii=S0022247X16305996&_rdoc=1&_issn=0022247X&md5=091856ef2b1c5127cd1da0827afa427b" title="Click to view the MathML source">L^p(T)n>n class="mathContainer hidden">n class="mathCode">$L^p\left(T\right)$n>n>n> with n id="mmlsi19" class="mathmlsrc">n class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X16305996&_mathId=si19.gif&_user=111111111&_pii=S0022247X16305996&_rdoc=1&_issn=0022247X&md5=deb58bba5d514952f0cda7989101d664" title="Click to view the MathML source">p∈[1,∞]n>n class="mathContainer hidden">n class="mathCode">n>n>n>.