Atomicity in injective Banach lattices
Vladikavkazskij matematičeskij žurnal, Tome 17 (2015) no. 3, pp. 44-52 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

This note is aimed to examine a Boolean valued interpretation of the concept of atomic Banach lattice and to give a complete description of the corresponding class of injective Banach lattices.
@article{VMJ_2015_17_3_a4,
     author = {A. G. Kusraev},
     title = {Atomicity in injective {Banach} lattices},
     journal = {Vladikavkazskij matemati\v{c}eskij \v{z}urnal},
     pages = {44--52},
     year = {2015},
     volume = {17},
     number = {3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/VMJ_2015_17_3_a4/}
}
TY  - JOUR
AU  - A. G. Kusraev
TI  - Atomicity in injective Banach lattices
JO  - Vladikavkazskij matematičeskij žurnal
PY  - 2015
SP  - 44
EP  - 52
VL  - 17
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/VMJ_2015_17_3_a4/
LA  - en
ID  - VMJ_2015_17_3_a4
ER  - 
%0 Journal Article
%A A. G. Kusraev
%T Atomicity in injective Banach lattices
%J Vladikavkazskij matematičeskij žurnal
%D 2015
%P 44-52
%V 17
%N 3
%U http://geodesic.mathdoc.fr/item/VMJ_2015_17_3_a4/
%G en
%F VMJ_2015_17_3_a4
A. G. Kusraev. Atomicity in injective Banach lattices. Vladikavkazskij matematičeskij žurnal, Tome 17 (2015) no. 3, pp. 44-52. http://geodesic.mathdoc.fr/item/VMJ_2015_17_3_a4/

[1] Kusraev A. G., “Boolean valued analysis and injective Banach lattices”, Dokl. RAS, 444:2 (2012), 143–145 | MR | Zbl

[2] Kusraev A. G., “Classification of injective Banach lattices”, Dokl. RAS, 453:1 (2013), 12–16 | MR | Zbl

[3] Kusraev A. G., Kutateladze S. S., Boolean Valued Analysis: Selected Topics, Trends in Science. The South of Russia, Vladikavkaz Scientific Center Press, Vladikavkaz, 2014, iv+400 pp.

[4] Aliprantis C. D., Burkinshaw O., Positive Operators, Acad. Press Inc., London etc., 1985, xvi+367 pp. | MR | Zbl

[5] Meyer-Nieberg P., Banach Lattices, Springer, Berlin etc., 1991, xvi+395 pp. | MR | Zbl

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

[7] Cartwright D. I., Extensions of positive operators between Banach lattices, Memoirs Amer. Math. Soc., 164, 1975, 48 pp. | MR | Zbl

[8] Haydon R., “Injective Banach lattices”, Math. Z., 156 (1974), 19–47 | DOI | MR

[9] Kusraev A. G., “A Boolean transfer principle for injective Banach lattices”, Sib. Mat. Zh., 56:5 (2015), 1111–1129 | DOI

[10] Kusraev A. G., Kutateladze S. S., Introduction to Boolean Valued Analysis, Nauka, M., 2005, 526 pp. (in Russian) | MR | Zbl

[11] Gordon E. I., “Real numbers in Boolean-valued models of set theory and $K$-spaces”, Dokl. Akad. Nauk SSSR, 237:4 (1977), 773–775 | MR | Zbl

[12] Kusraev A. G., Dominated Operators, Nauka, M., 2003, 619 pp. (in Russian) | MR

[13] Luxemburg W. A. J., Zaanen A. C., Riesz Spaces, v. 1, North-Holland, Amsterdam–London, 1971, 514 pp. | MR | Zbl