Zur allgemeinen Theorie der halbgeordneten Räume Original Research Article

Foreword by K. Kopotun1Correspondence to: K. Kopotun, Department of Mathematics, University of Manitoba, Winnipeg, Manitoba, Canada ^^IR3T 2N2. Email: . The paper “On the general theory of semi-ordered spaces” (“Zur allgemeinen Theorie der halbgeordneten Räume”) was written by L.V. Kantorovich and G.R. Lorentz sometime in 1937–1939, and this is the first time it appears in print. The following is a short history of this manuscript. In his letter to I.P. Natanson written on October 11, 1937, G.G. Lorentz mentioned a talk on joint work with L.V. Kantorovich that he gave at a Session on Functional Analysis in Moscow earlier that year. The records of the Academy of Sciences of USSR indicate that a Session on Functional Analysis took place in Moscow during September 27–29, 1937, and that G.R. Lorentz gave a talk “Topological theory of semi-ordered spaces” there, and that L.V. Kantorovich was speaking on “Theory of linear operations in semi-ordered spaces”. The manuscript “On the general theory of semi-ordered spaces” was found in the archives of L.V. Kantorovich. According to Vsevolod Leonidovich Kantorovich, L.V. Kantorovich’s son, it was submitted to Trudy Tomskogo Gosudarstvennogo Universiteta imeni V. V. Kuibysheva (Proceedings of Tomsk State University). The typed version of the manuscript has a handwritten note by N. Romanov dated by August 31, 1939 stating that the manuscript is accepted for publication. The manuscript was never published (probably because of the World War II) and around 1945 was returned to L.V. Kantorovich. It has been decided to publish this manuscript in its original language (German), and translate the extended abstract accompanying this manuscript from Russian to English. The manuscript appears here in its original form with only minor editorial corrections. Publication of this historical document would not have been possible without the assistance and effort of many people. In particular, the significant help of C. de Boor, Ya.I. Fet, V.L. Kantorovich, V.N. Konovalov, and S.S. Kutateladze is acknowledged and greatly appreciated.