On subspaces of Banach spaces where every functional has a unique norm-preserving extension

Studia Mathematica

Volumn 117, Issue 3, 1996, Pages 289-306

  Oja, Eve ^a   Põldvere, MÄRT ^a  

^a UNIVERSITY OF TARTU   (Estonia)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001549807     PISSN: 00393223     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (31)

1. T. Andô, On some properties of convex functions. Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 8 (1960), 413-418.
2. B. Beauzamy, Introduction to Banach Spaces and Their Geometry, North-Holland Math. Stud. 68, North-Holland, Amsterdam, 1982.
3. B. Beauzamy et B. Maurey, Points minimaux et ensembles optimaux dans les espaces de Banach, J. Funct. Anal. 24 (1977), 107-139.
4. P. K. Belobrov, Minimal extension of linear functional to second dual spaces, Mat. Zametki 27 (1980), 439-445 (in Russian).
5. P. G. Casazza and N. J. Kalton, Notes on approximation properties in separable Banach spaces, in: Geometry of Banach Spaces, Proc. Conf. Strobl 1989, P. F. X. Müller and W. Schachermayer (eds.). London Math. Soc. Lecture Note Ser. 158, Cambridge Univ. Press, 1990, 49-63.
6. S. R. Foguel, On a theorem by A. E. Taylor, Proc. Amer. Math. Soc. 9 (1958), 325.
7. G. Godefroy, Points de Namioka, espaces normants, applications à la théorie isométrique de la dualité, Israel J. Math. 38 (1981), 209-220.
8. G. Godefroy, N. J. Kalton et P. D. Saphar, Idéaux inconditionnels dans les espaces de Banach, C. R. Acad. Sci. Paris Sér. I 313 (1991), 845-849.
9. _, _, _, Unconditional ideals in Banach spaces, Studia Math. 104 (1993), 13-59.
10. P. Harmand, D. Werner, and W. Werner, M-Ideals in Banach Spaces and Banach Algebras, Lecture Notes in Math. 1547, Springer, Berlin, 1993.
11. J. Hennefeld, M-ideals, HB-subspaces, and compact operators, Indiana Univ. Math. J. 28 (1979), 927-934.
12. J. Johnson, Remarks on Banach spaces of compact operators, J. Funct. Anal. 32 (1979), 304-311.
13. Å. Lima, Intersection properties of balls and subspaces in Banach spaces, Trans. Amer. Math. Soc. 227 (1977), 1-62.
14. _, M-ideals of compact operators in classical Banach spaces, Math. Scand. 44 (1979), 207-217.
15. _, Uniqueness of Hahn-Banach extensions and liftings of linear dependences, ibid. 53 (1983), 97-113.
16. Å. Lima, E. Oja, T. S. S. R. K. Rao, and D. Werner, Geometry of operator spaces, Michigan Math. J. 41 (1994), 473-490.
17. Å. Lima and U. Uttersrud, Centers of symmetry infinite intersections of balls in Banach spaces, Israel J. Math. 44 (1983), 189-200.
18. E. Oja, On the uniqueness of the norm preserving extension of a linear functional in the Hahn-Banach theorem, Izv. Akad. Nauk Est. SSR Ser. Fiz. Mat. 33 (1984), 424-438 (in Russian).
19. _, Strong uniqueness of the extension of linear continuous functionals according to the Hahn-Banach theorem, Mat. Zametki 43 (1988), 237-246 (in Russian); English transi.: Math. Notes 43 (1988), 134-139.
20. _, Strong uniqueness of the extension of linear continuous functionals according to the Hahn-Banach theorem, Mat. Zametki 43 (1988), 237-246 (in Russian); English transi.: Math. Notes 43 (1988), 134-139.
21. _, Dual de l'espace des opérateurs linéaires continus, C. R. Acad. Sci. Paris Sér. I 309 (1989), 983-986.
22. _, HB-subspaces and Godun sets of subspaces in Banach spaces, preprint, 1995.
23. R. R. Phelps, Uniqueness of Hahn-Banach extensions and unique best approximation, Trans. Amer. Math. Soc. 95 (1960), 238-255.
24. M. M. Rao and Z. D. Ren, Theory of Orlicz Spaces, Dekker, New York, 1991.
25. I. Singer, Best Approximation in Normed Linear Spaces by Elements of Linear Subspaces, Grundlehren Math. Wiss. 171, Springer, Berlin, 1970.
26. M. A. Smith and F. Sullivan, Extremely smooth Banach spaces, in: Banach Spaces of Analytic Functions, Proc. Conf. Kent, Ohio, 1976, J. Baker, C. Cleaver, and J. Diestel (eds.), Lecture Notes in Math. 604, Springer, Berlin, 1977, 125-137.
27. F. Sullivan, Geometrical properties determined by the higher duals of a Banach space, Illinois J. Math. 21 (1977), 315-331.
28. A. E. Taylor, The extension of linear functionals, Duke Math. J. 5 (1939), 538-547.
29. S. L. Troyanski, An example of a smooth space whose dual is not strictly normed, Studia Math. 35 (1970), 305-309 (in Russian).
30. L. P. Vlasov, Approximative properties of sets in normed linear spaces, Uspekhi Mat. Nauk 28 (6) (1973), 3-66 (in Russian).
31. D. Werner, M-ideals and the "basic inequality", J. Approx. Theory 76 (1994), 21-30.