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DOI: 10.23671/VNC.2016.1.5947
Operators on Injective Banach Lattices
Kusraev, A. G.
Vladikavkaz Mathematical Journal 2016. Vol. 18. Issue 1.
Abstract: The paper deals with some properties of bounded linear operators on injective Banach lattice using a Boolean-valued transfer principle from \(AL\)-spaces to injectives stated in author's previous work.
For citation: Kusraev A. G. Operators on injective Banach lattices // Vladikavkazskii
matematicheskii zhurnal [Vladikavkaz Math. J.], vol. 19, no. 1, pp.
42-50.
DOI 10.23671/VNC.2016.1.5947
1. Kusraev A. G. Boolean valued transfer principle for injective
Banach lattices. Siberian Math. J, 2015, vol. 56, no 5. pp. 1111-1129.
2. Abramovich Yu. A. Weakly compact sets in topological Dedekind complete vector lattices. Teor. Funkcii , Funkcional. Anal. i Prilozen, 1972, vol. 15,
pp. 27-35.
3. Lotz H. P. Extensions and liftings of positive linear mappings on Banach lattices. Trans. Amer. Math. Soc., 1975, vol. 211, pp. 85-100.
4. Meyer-Nieberg P. Banach Lattices. Springer: Berlin etc., 1991. xvi+395 p.
5. Haydon R. Injective Banach lattices. Math. Z., 1974, vol. 156, pp. 19-47.
6. Aliprantis C. D. and Burkinshaw O. Positive Operators. N. Y.: Acad. Press, 1985. xvi+367 p.
7. Kusraev A. G. Dominated Operators. Dordrecht: Kluwer, 2000. 405 p.
8. Kusraev A. G. and Kutateladze S. S. Boolean Valued Analysis: Selected Topics. Vladikavkaz: SMI VSC RAS, 2014. iv+400 p.
9. Bell J. L. Boolean-Valued Models and Independence Proofs in Set Theory. N. Y. etc.: Clarendon Press, 1985. xx+165 p.
10. Kusraev A. G. and Kutateladze S. S. Boolean valued analysis. Dordrecht a.o.: Kluwer, 1995.
11. Takeuti G. and Zaring W. M. Axiomatic Set Theory. N. Y.: Springer-Verlag, 1973. 238 p.
12. Gutman A. E. Banach bundles in the theory of lattice-normed spaces. Linear Operators Compatible with Order. Novosibirsk: Sobolev Institute Press, 1995, pp. 63-211. [in Russian].
13. Gutman A. E. Disjointness preserving operators.Vector Lattices and Integral Operators / Ed. S. S. Kutateladze. Dordrecht etc.: Kluwer Acad. Publ., 1996, pp. 361-454.
14. Abramovich Y. A. and Aliprantis C. D. An Invitation to Operator Theory. Providence (R.I.): Amer. Math. Soc, 2002. iv+530 p.
15. Abramovich Y. A. A generalization of a theorem of J. Holub. Proc. Amer. Math. Soc., 1990, vol. 108, pp. 937-939.
16. Schmidt K. D. Daugavet's equation and orthomorphisms. Proc. Amer. Math. Soc., 1990, vol. 108, pp. 905-911.
17. Lindenstrauss J. and Tzafriri L. Classical Banach Spaces. Vol. 2. Function Spaces. Berlin etc.: Springer-Verlag, 1979. 243 p.
18. Schep A. R. Daugavet type inequality for operators on \(L^p\)-spaces. Positivity, 2003, vol. 7 (1-2), pp. 103-111.
19. Kusraev A. G. Kantorovich's Principle in Action: \(AW^\ast\)-modules and injective Banach lattices. Vladikavkaz Math. J., 2012, vol. 14, no. 1, pp. 67-74.
20. Gutman A. E. and Lisovskaya S. A. The boundedness principle for lattice-normed. Siberian Math. J., 2009, vol. 50 (5), pp. 830-837.
21. Shvidkoy R. V. The largest linear space of operators satisfying the Daugavet equation in \(L_1\). Proc. Amer. Math., 2002, vol. 120 (3), pp. 773-777.
22. Wickstead A. W. \(AL\)-spaces and \(AM\)-spaces of operators. Positivity, 2000, vol. 4 (3), pp. 303-311.
23. Kusraev A. G. Boolean Valued Analysis Approach to Injective Banach Lattices. Vladikavkaz: Southern Math. Inst. VSC RAS, 2011. 28 p. (Preprint ¹ 1).
24. Schaefer H. H. Banach Lattices and Positive Operators. Berlin etc.: Springer-Verlag, 1974. 376 p.
25. Diestel J., Jarchow H., and Tonge A. Absolutely Summing Operators. Cambridge etc.: Cambridge Univ. Press, 1995. xv+474 p.
26. Levin V. L. Tensor products and functors in categories of Banach spaces determined by \(K\!B\)-lineals. Dokl. Acad. Nauk SSSR, 1965, vol. 163 (5), pp. 1058-1060.
