\(L^p\)-spaces with respect to conditional expectation on Riesz spaces (Q342908)

The authors consider a Dedekind complete Riesz space \(E\), and a linear operator \(T\) on \(E\) being the conditional expectation. Then \(L^1(T)\) is the natural domain of \(T\), and \(L^p(T)= \{x\in L^1(T):| x| ^p\in L^1(T)\}\), \(p\in[1,\infty]\). Some inequalities on \(L^p(T)\) are presented generalizing the corresponding result known for \(p=2\) [\textit{W.-C. Kuo} et al., ibid. 303, No. 2, 509--521 (2005; Zbl 1075.46002)].