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DOI: 10.23671/VNC.2017.3.7263
Atomicity in Injective Banach Lattices
Kusraev, A. G.
Vladikavkaz Mathematical Journal 2015. Vol. 17. Issue 3.
Abstract: 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.
For citation: Kusraev A. G. Atomicity in Injective Banach Lattices. Vladikavkazskii matematicheskii zhurnal [Vladikavkaz Math. J.], vol. 17, no. 3, pp.44-52.
DOI 10.23671/VNC.2017.3.7263
1. Kusraev A. G. Boolean valued analysis and injective Banach
lattices. Dokl. RAS, 2012, vol. 444, no. 2, pp. 143-145.
2. Kusraev A. G. Classification of injective Banach lattices. Dokl.
RAS, 2013, vol. 453, no. 1, pp. 12-16.
3. Kusraev A. G. and Kutateladze S. S. Boolean Valued Analysis:
Selected Topics, Vladikavkaz, Vladikavkaz Scientific Center Press,
2014, iv+400 p. (Trends in Science. The South of Russia).
4. Aliprantis C. D. and Burkinshaw O. Positive Operators, London
etc.: Acad. Press Inc., 1985, xvi+367 p.
5. Meyer-Nieberg P. Banach Lattices, Berlin etc.: Springer, 1991,
xvi+395 p.
6. Lotz H. P. Extensions and liftings of positive linear mappings on
Banach lattices. Trans. Amer. Math. Soc., 1975, vol. 211, pp.
85-100.
7. Cartwright D. I. Extension of positive operators between Banach
lattices. Memoirs Amer. Math. Soc., 1975, 164 p.
8. Haydon R. Injective Banach lattices. Math. Z., 1974, vol. 156,
pp. 19-47.
9. Kusraev A. G. A Boolean transfer principle for injective Banach
lattices. Sib. Mat. Zh., 2015, vol. 56, no. 5, [DOI
10.17377/smzh.2015.56.511].
10. Kusraev A. G. and Kutateladze S. S. Introduction to Boolean
Valued Analysis, M., Nauka, 2005, 526 p. (in Russian).
11. Gordon E. I. Real numbers in Boolean-valued models of set theory
and K-spaces. Dokl. Akad. Nauk SSSR, 1977, vol. 237, no. 4, pp.
773-775.
12. Kusraev A. G. Dominated Operators, Ì., Nauka, 2003, 619 p. (in
Russian).
13. Luxemburg W. A. J. and Zaanen A. C. Riesz Spaces. Vol. 1,
Amsterdam and London, North-Holland, 1971, 514 p.