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K-space

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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


Comments

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)
How to Cite This Entry:
K-space. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=K-space&oldid=32046
This article was adapted from an original article by M.I. Voitsekhovskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article