Geodesic
Monotone Semigroups of Operators on Cones*
Canadian mathematical bulletin, Tome 12 (1969) no. 3, pp. 299-309

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In this paper we consider a special class of linear operators defined on a cone K in a Banach space X. This class of operators is the natural generalization of a class of operators which has applications in the theory of interpolation spaces. In particular, using the criteria developed in Theorem 1, it is possible to characterize those sequence spaces X such that every linear operator A of weak types (p, p) and (q, q) is a continuous mapping of X into itself. For details of this we refer the reader to [3]. 
Boyd, David W. Monotone Semigroups of Operators on Cones*. Canadian mathematical bulletin, Tome 12 (1969) no. 3, pp. 299-309. doi: 10.4153/CMB-1969-038-3
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     author = {Boyd, David W.},
     title = {Monotone {Semigroups} of {Operators} on {Cones*}},
     journal = {Canadian mathematical bulletin},
     pages = {299--309},
     year = {1969},
     volume = {12},
     number = {3},
     doi = {10.4153/CMB-1969-038-3},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1969-038-3/}
}
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