Difference between revisions of "K-space"
From Encyclopedia of Mathematics
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''Kantorovich space'' | ''Kantorovich space'' | ||
| − | An ordered complete vector space, i.e. a semi-ordered vector space (cf. [[ | + | 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 [[#References|[1]]]. |
====References==== | ====References==== | ||
| − | <table><TR><TD valign="top">[1]</TD> <TD valign="top"> | + | <table> |
| − | + | <TR><TD valign="top">[1]</TD> <TD valign="top"> L.V. Kantorovich, "Lineare halbgeordnete Räume" ''Mat. Sb.'' , '''2''' (1937) pp. 121–165</TD></TR> | |
| − | + | <TR><TD valign="top">[a1]</TD> <TD valign="top"> H. Freudenthal, "Teilweise geordnete Moduln" ''Proc. K. Ned. Akad. Wetensch. Amsterdam'' , '''39''' (1936) pp. 641–651</TD></TR> | |
| − | + | <TR><TD valign="top">[a2]</TD> <TD valign="top"> F. Riesz, "Sur quelques notions fondamentales dans la théorie générale des opérations linéaires" ''Ann. of Math.'' , '''41''' (1940) pp. 174–206</TD></TR> | |
| − | + | <TR><TD valign="top">[a3]</TD> <TD valign="top"> S.W.P. Steen, "An introduction to the theory of operators I" ''Proc. London Math. Soc. (2)'' , '''41''' (1936) pp. 361–392</TD></TR> | |
| − | + | <TR><TD valign="top">[a4]</TD> <TD valign="top"> W.A.J. Luxemburg, A.C. Zaanen, "Riesz spaces" , '''I''' , North-Holland (1971)</TD></TR> | |
| − | + | <TR><TD valign="top">[a5]</TD> <TD valign="top"> A.C. Zaanen, "Riesz spaces" , '''II''' , North-Holland (1983)</TD></TR><TR><TD valign="top">[a6]</TD> <TD valign="top"> H.H. Schaefer, "Banach lattices and positive operators" , Springer (1974)</TD></TR> | |
| − | + | <TR><TD valign="top">[a7]</TD> <TD valign="top"> B.Z. Vulikh, "Introduction to the theory of partially ordered spaces" , Wolters-Noordhoff (1967) (Translated from Russian)</TD></TR> | |
| − | + | </table> | |
====See also==== | ====See also==== | ||
[[Kelley space]] | [[Kelley space]] | ||
Revision as of 09:25, 3 August 2025
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 |
| [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) |
See also
How to Cite This Entry:
K-space. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=K-space&oldid=56197
K-space. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=K-space&oldid=56197
This article was adapted from an original article by M.I. Voitsekhovskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article