Geodesic
Functional calculus and Minkowski duality on vector lattices
Vladikavkazskij matematičeskij žurnal, Tome 11 (2009) no. 2, pp. 31-42

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The paper extends homogeneous functional calculus on vector lattices. It is shown that the function of elements of a relatively uniformly complete vector lattice can naturally be defined if the positively homogeneous function is defined on some conic set and is continuous on some closed convex subcone. An interplay between Minkowski duality and homogeneous functional calculus leads to the envelope representation of abstract convex elements generated by the linear hull of a finite collection in a uniformly complete vector lattice. 
@article{VMJ_2009_11_2_a4,
     author = {A. G. Kusraev},
     title = {Functional calculus and {Minkowski} duality on vector lattices},
     journal = {Vladikavkazskij matemati\v{c}eskij \v{z}urnal},
     pages = {31--42},
     publisher = {mathdoc},
     volume = {11},
     number = {2},
     year = {2009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/VMJ_2009_11_2_a4/}
}
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A. G. Kusraev. Functional calculus and Minkowski duality on vector lattices. Vladikavkazskij matematičeskij žurnal, Tome 11 (2009) no. 2, pp. 31-42. http://geodesic.mathdoc.fr/item/VMJ_2009_11_2_a4/