Some open problems on Banach spaces

Author A. M. Plichko, M. M. Popov
aplichko@pk.edu.pl, misham.popov@gmail.com
Politechnika Krakowska im. Tadeusza Kosciuszko, Chernivtsi National University

Abstract Notes of the Problem Session which has been held on the section of Banach Spaces during the International conference dedicated to the 120-th anniversary of Stefan Banach in Lviv (Ukraine), September 17–21, 2012.
Keywords Banach space; Banach lattice
Reference 1. V.M. Kadets, Some remarks concerning the Daugavet equation, Quaestiones Math., 19 (1996), 225–235.

2. V.M. Kadets, R.V. Shvidkoy, G.G. Sirotkin, D. Werner, Banach spaces with the Daugavet property, Trans. Amer. Math. Soc., 352 (2000), 855–873.

3. V.M. Kadets, R.V. Shvidkoy, G.G. Sirotkin, D. Werner, Banach spaces with the Daugavet property, Trans. Amer. Math. Soc., 352 (2000), 855–873.

4. T. Oikhberg, The Daugavet property of $C^*$-algebras and non-commutative $L_p$-spaces, Positivity, 6 (2002), 59–73.

5. I.V. Krasikova, On a generalization of the notion of a compact operator on the spaces $L_p$, Nauk. Visn. Chern. Nat. Univ., 501 (2010), P. 38–42.

6. B. Maurey Sous-espaces complementes de $L^p$ d’apres P. Enflo, Semin. Maurey-Schwartz, Paris, 1974- 75, Exp. III. (1975), P. 1–14.

7. A.M. Plichko, M.M. Popov, Symmetric function spaces on atomless probability spaces, Diss. Math. (Rozpr. mat.), 306 (1990), P. 1–85.

8. M. Popov, B. Randrianantoanina, Narrow Operators on Function Spaces and Vector Lattices, De Gruyter Studies in Mathematics 45, Berlin, De Gruyter, 2012.

9. J. Lindenstrauss, L. Tzafriri, On the isomorphic classification of injective Banach lattices, Advances Math., 7B (1981), 489–498.

10. P.J. Mangheni, The classification of injective Banach lattices, Israel J. Math., 48 (1984), 341–347.

11. J. Lindenstrauss, D.E. Wulbert, On the classification of he Banach spaces whose duals are $L_1$-spaces, J. Funct. Anal., 4 (1969), 332–349.

12. A.G. Kusraev, Boolean-valued analysis and injective Banach lattices, Doklady Ross. Akad. Nauk, 444 (2012), Ή2, 143–145 (in Russian). English translated in Doklady Mathematics, 85 (2012), 341–343.

13. H.B. Cohen, Injective envelopes of Banach spaces, Bull. Amer. Math. Soc., 70 (1964), 723–726.

14. A. Lima, V. Lima, E. Oja, Bounded approximation properties via integral and nuclear operators, Proc. Amer. Math. Soc., 138 (2010), 287–297.

15. A. Lima, E. Oja, The weak metric approximation property, Math. Ann., 333 (2005), 471–484.

16. A. Lissitsin, A unified approach to the strong and the weak bounded approximation properties of Banach spaces, Studia Math. (to appear)

17. E. Oja, On bounded approximation properties of Banach spaces, Banach Center Publ., 91 (2010), 219–231.

18. E. Oja, Bounded approximation properties via Banach operator ideals, Advanced Courses of Mathematical Analysis IV, 196–215, World Sci. Publ., Hackensack, NJ, 2012.

19. A.M. Plichko, D. Yost, Complemented and uncomplemented subspaces of Banach spaces, Extracta Math., 15 (2000), 335–371.

20. M.D. Asadi, Stinspring’s theorem for Hilbert $C^*$-modules, J. Operator Theory, 62 (2009), Ή2, 235–238.

21. M. Pliev, Stinespring type theorem for completely n-positive maps on Hilbert $C^*$-modules, Submitted.

22. M. Joita, Covariant version of the Stinespring type theorem for Hilbert $C^*$-modules, Cent. Eur. J. Math., 13 (2011), 803–813.

23. M. Joita, Comparision of completely positive maps on Hilbert $C^*$-modules, Preprint, arXiv:1201.0593v1.

24. F. Stinspring, Positive functions on $C^*$-algebras, Proc. Amer. Math. Soc., 2 (1955), 211–216.

25. V. Mykhaylyuk, M. Popov, B. Randrianantoanina, G. Schechtman, Narrow and $l_2$-strictly singular operators from $L_p$, Preprint.

26. A.M. Plichko, M.M. Popov, Symmetric function spaces on atomless probability spaces, Diss. Math. (Rozpr. mat.), 306 (1990), 1–85.

27. M. Popov, B. Randrianantoanina, Narrow Operators on Function Spaces and Vector Lattices. De Gruyter Studies in Mathematics 45, Berlin, De Gruyter, 2012.

Pages 203-211
Volume 38
Issue 2
Year 2012
Journal Matematychni Studii
Full text of paper PDF
Table of content of issue HTML