Geodesic
Dilations of Positive Contractions on Lp Spaces*
Canadian mathematical bulletin, Tome 20 (1977) no. 3, pp. 285-292

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Throughout this article p denotes a fixed number such that 1 ≤ p < ∞. The definition of a real Lp space associated with a measure space is well known. These spaces are Banach Spaces and, with the usual partial ordering of (equivalence classes of) functions, also Banach Lattices. 
Akcoglu, M. A.; Sucheston, L. Dilations of Positive Contractions on Lp Spaces*. Canadian mathematical bulletin, Tome 20 (1977) no. 3, pp. 285-292. doi: 10.4153/CMB-1977-044-4
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     title = {Dilations of {Positive} {Contractions} on {Lp} {Spaces*}},
     journal = {Canadian mathematical bulletin},
     pages = {285--292},
     year = {1977},
     volume = {20},
     number = {3},
     doi = {10.4153/CMB-1977-044-4},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1977-044-4/}
}
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