Banach lattices of continuous sections

Author: Kusraev Anatoly G., Tabuev Soslan N.

Article in issue: 4 т.14, 2012.

Free access

The aim of this note is to outline some application of ample continuous Banach bundles to the theory of Banach lattices.

Banach lattice, continuous banach bundle

Short address: https://sciup.org/14318398

IDR: 14318398 | UDC: 512.555+517.982

Банаховы решетки непрерывных сечений

Заметка представляет собой набросок некоторых приложений просторных банаховых расслоений к~теории банаховых решеток.

Gierz G. Darstellung von Banachverbanden durch Schnitte in Bundeln//Mitt. Math. Sem. Univ. Giessen.-1977.-Vol. 125.
Gierz G. Bundles of Topological Vector Spaces and Their Duality.-Berlin etc.: Springer-Verlag, 1982.
Gutman A. E. Banach bundles in the theory of lattice-normed spaces. I. Continuous Banach bundles//Siberian Adv. Math.-1993.-Vol. 3, № 3.-P. 1-55.
Gutman A. E. Banach bundles in the theory of lattice-normed spaces. II. Measurable Banach bundles//Siberian Adv. Math.-1993.-Vol. 3, № 4.-P. 8-40.
Ganiev I. G. Measurable bundles of lattices and their applications//Studies on functional analysis and its applications.-Moscow: Nauka, 2006.-P. 9-49.
Kusraev A. G. Measurable bundles of Banach lattices//Positivity.-2010.-Vol. 14.-P. 785-799.
Kusraev A. G. Dominated Operators.-Dordrecht: Kluwer, 2000.-446 p.
Lotz H. P. Extensions and liftings of positive linear mappings on Banach lattices//Trans. Amer. Math. Soc.-1975.-Vol. 211.-P. 85-100.
Cartwright D. I. Extension of positive operators between Banach lattices//Memoirs Amer. Math. Soc.-1975.-Vol. 164.-P. 1-48.
Haydon R. Injective Banach lattices//Math. Z.-1977.-Vol. 156.-P. 19-47.
Kusraev A. G. Boolean Valued Analysis Approach to Injective Banach Lattices.-Vladikavkaz: Southern Math. Inst. VSC RAS, 2011.-28 p.-(Preprint № 1).
Kusraev A. G. Boolean-valued analysis and injective Banach lattices//Doklady Ross. Akad. Nauk.-2012.-Vol. 444, № 2.-P. 143-145; Engl. transl.: Doklady Mathematics.-2012.-Vol. 85, № 3.-P. 341-343.