The de Schipper formula and squares of Riesz spaces (Q2385787)

Starting with an arbitrary Riesz space, the authors construct first the square mean closed Riesz space and after it geometric closed Riesz space. They prove that every geometric mean closed Riesz space is square mean closed, but the converse is not true. They generalize the de Schipper formula [\textit{W.\,J.\,de Schipper}, Nederl.\ Akad.\ Wet., Proc., Ser.\,A, Indag.\ Math.\ 2, 423--436 (1973; Zbl 0268.47041)] and they fit completely in the programme by \textit{A.\,C.\thinspace Zaanen} [``Riesz spaces.\ II'' (Amsterdam-New York-Oxford: North--Holland Publishing Company) (1983; Zbl 0519.46001)].