K-space

Kantorovich space

An ordered complete vector space, i.e. a semi-ordered vector space (cf. Semi-ordered space) in which every set that is bounded from above has a supremum. This notion was introduced by L.V. Kantorovich [1].

References

[1]	L.V. Kantorovich, "Lineare halbgeordnete Räume" Mat. Sb. , 2 (1937) pp. 121–165

References

[a1]	H. Freudenthal, "Teilweise geordnete Moduln" Proc. K. Ned. Akad. Wetensch. Amsterdam , 39 (1936) pp. 641–651
[a2]	F. Riesz, "Sur quelques notions fondamentales dans la théorie générale des opérations linéaires" Ann. of Math. , 41 (1940) pp. 174–206
[a3]	S.W.P. Steen, "An introduction to the theory of operators I" Proc. London Math. Soc. (2) , 41 (1936) pp. 361–392
[a4]	W.A.J. Luxemburg, A.C. Zaanen, "Riesz spaces" , I , North-Holland (1971)
[a5]	A.C. Zaanen, "Riesz spaces" , II , North-Holland (1983)
[a6]	H.H. Schaefer, "Banach lattices and positive operators" , Springer (1974)
[a7]	B.Z. Vulikh, "Introduction to the theory of partially ordered spaces" , Wolters-Noordhoff (1967) (Translated from Russian)