Banach lattices of continuous sections
Vladikavkazskij matematičeskij žurnal, Tome 14 (2012) no. 4, pp. 41-44 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The aim of this note is to outline some application of ample continuous Banach bundles to the theory of Banach lattices.
@article{VMJ_2012_14_4_a5,
     author = {A. G. Kusraev and S. N. Tabuev},
     title = {Banach lattices of continuous sections},
     journal = {Vladikavkazskij matemati\v{c}eskij \v{z}urnal},
     pages = {41--44},
     year = {2012},
     volume = {14},
     number = {4},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/VMJ_2012_14_4_a5/}
}
TY  - JOUR
AU  - A. G. Kusraev
AU  - S. N. Tabuev
TI  - Banach lattices of continuous sections
JO  - Vladikavkazskij matematičeskij žurnal
PY  - 2012
SP  - 41
EP  - 44
VL  - 14
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/VMJ_2012_14_4_a5/
LA  - en
ID  - VMJ_2012_14_4_a5
ER  - 
%0 Journal Article
%A A. G. Kusraev
%A S. N. Tabuev
%T Banach lattices of continuous sections
%J Vladikavkazskij matematičeskij žurnal
%D 2012
%P 41-44
%V 14
%N 4
%U http://geodesic.mathdoc.fr/item/VMJ_2012_14_4_a5/
%G en
%F VMJ_2012_14_4_a5
A. G. Kusraev; S. N. Tabuev. Banach lattices of continuous sections. Vladikavkazskij matematičeskij žurnal, Tome 14 (2012) no. 4, pp. 41-44. http://geodesic.mathdoc.fr/item/VMJ_2012_14_4_a5/

[1] Gierz G., Darstellung von Banachverbänden durch Schnitte in Bündeln, Mitt. Math. Sem. Univ. Giessen., 125, 1977 | MR

[2] Gierz G., Bundles of Topological Vector Spaces and Their Duality, Springer-Verlag, Berlin etc., 1982 | MR | Zbl

[3] Gutman A. E., “Banach bundles in the theory of lattice-normed spaces. I. Continuous Banach bundles”, Siberian Adv. Math., 3:3 (1993), 1–55 | MR | Zbl

[4] Gutman A. E., “Banach bundles in the theory of lattice-normed spaces. II. Measurable Banach bundles”, Siberian Adv. Math., 3:4 (1993), 8–40 | MR | Zbl

[5] Ganiev I. G., “Measurable bundles of lattices and their applications”, Studies on functional analysis and its applications, Nauka, Moscow, 2006, 9–49 | MR

[6] Kusraev A. G., “Measurable bundles of Banach lattices”, Positivity, 14 (2010), 785–799 | DOI | MR | Zbl

[7] Kusraev A. G., Dominated Operators, Kluwer, Dordrecht, 2000, 446 pp. | MR | Zbl

[8] Lotz H. P., “Extensions and liftings of positive linear mappings on Banach lattices”, Trans. Amer. Math. Soc., 211 (1975), 85–100 | DOI | MR | Zbl

[9] Cartwright D. I., “Extension of positive operators between Banach lattices”, Memoirs Amer. Math. Soc., 164 (1975), 1–48 | MR

[10] Haydon R., “Injective Banach lattices”, Math. Z., 156 (1977), 19–47 | DOI | MR | Zbl

[11] Kusraev A. G., Boolean Valued Analysis Approach to Injective Banach Lattices, Preprint No 1, Southern Math. Inst. VSC RAS, Vladikavkaz, 2011, 28 pp.

[12] Doklady Mathematics, 85:3 (2012), 341–343 | DOI | MR | Zbl