Positivity 7: 87–93, 2003. © 2003 Kluwer Academic Publishers. Printed in the Netherlands. Extension Theorems and the Riesz Decomposition Property A Short Survey on the Results Obtained by the Authors in Recent Years ˘ ˘ NICOLAE DANET ¸ and RODICA-MIHAELA DANET ¸ Technical University of Civil Engineering of Bucharest, 122–124 Lacul Tei Blvd., Bucharest 38, 72302 Romania. E-mail: email@example.com Mathematics Subject Classiﬁcation (2000): Primary: 47B60; Secondary: 47B65, 46A22, 46B42. Key words: Banach lattices, Hahn–Banach Theorem, odered vector spaces, regular operators. 1. Some Deﬁnitions and Notations An ordered vector space F has the Riesz decomposition property (RDP in short) if for any positive elements z, x ,x with z x + x , there exist z ,z such that 1 2 1 2 1 2 0 z x , 0 z x and z = z + z . The RDP is equivalent with the 1 1 2 2 1 2 ﬁnite interpolation property, i.e., if x ,x z ,z then there exists y such that 1 2 1 2 x ,x y z ,z (, p. 129). Every Riesz space has the Riesz decomposition 1 2 1 2 property, but the
Positivity – Springer Journals
Published: Oct 17, 2004
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