Geometric Characterization of Injective Banach Lattices

Anatoly Kusraev and Semën Kutateladze
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Anatoly Kusraev: Southern Mathematical Institute and Khetagurov North-Ossetian State University, 44 Vatutina St., Vladikavkaz 362025, Russia
Semën Kutateladze: Sobolev Institute of Mathematics, 4 Koptyug Avenue, Novosibirsk 630090, Russia

Mathematics, 2021, vol. 9, issue 3, 1-18

Abstract: This is a continuation of the authors’ previous study of the geometric characterizations of the preduals of injective Banach lattices. We seek the properties of the unit ball of a Banach space which make the space isometric or isomorphic to an injective Banach lattice. The study bases on the Boolean valued transfer principle for injective Banach lattices. The latter states that each such lattice serves as an interpretation of an A L -space in an appropriate Boolean valued model of set theory. External identification of the internal Boolean valued properties of the corresponding A L -spaces yields a characterization of injective Banach lattices among Banach spaces and ordered Banach spaces. We also describe the structure of the dual space and present some dual characterization of injective Banach lattices.

Keywords: injective banach lattice; L-projection; M-projection; gordon’s theorem; boolean valued analysis; boolean valued representation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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