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1993 | 105 | 1 | 37-49
Tytuł artykułu

Total subspaces in dual Banach spaces which are not norming over any infinite-dimensional subspace

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The main result: the dual of separable Banach space X contains a total subspace which is not norming over any infinite-dimensional subspace of X if and only if X has a nonquasireflexive quotient space with a strictly singular quotient mapping.
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Opis fizyczny
  • [Al] A. A. Albanese, On total subspaces in duals of spaces of type C(K) or $L^1$, preprint.
  • [An] A. Andrew, James' quasi-reflexive space is not isomorphic to any subspace of its dual, Israel J. Math. 38 (1981), 276-282.
  • [B] S. Banach, Théorie des opérations linéaires, Monografje Mat. 1, Warszawa 1932.
  • [BDH] E. Behrends, S. Dierolf and P. Harmand, On a problem of Bellenot and Dubinsky, Math. Ann. 275 (1986), 337-339.
  • [CY] P. Civin and B. Yood, Quasi-reflexive spaces, Proc. Amer. Math. Soc. 8 (1957), 906-911.
  • [DJ] W. J. Davis and W. B. Johnson, Basic sequences and norming subspaces in non-quasi-reflexive Banach spaces, Israel J. Math. 14 (1973), 353-367.
  • [DL] W. J. Davis and J. Lindenstrauss, On total nonnorming subspaces, Proc. Amer. Math. Soc. 31 (1972), 109-111.
  • [DM] S. Dierolf and V. B. Moscatelli, A note on quojections, Funct. Approx. Comment. Math. 17 (1987), 131-138.
  • [D] J. Dixmier, Sur un théorème de Banach, Duke Math. J. 15 (1948), 1057-1071.
  • [DS] N. Dunford and J. T. Schwartz, Linear Operators, Part I: General Theory, Interscience, New York 1958.
  • [F] R. J. Fleming, Weak*-sequential closures and the characteristic of subspaces of conjugate Banach spaces, Studia Math. 26 (1966), 307-313.
  • [G] B. V. Godun, On weak* derived sets of sets of linear functionals, Mat. Zametki 23 (1978), 607-616 (in Russian).
  • [GR] B. V. Godun and S. A. Rakov, Banach-Saks property and the three space problem, ibid. 31 (1982), 61-74 (in Russian).
  • [Gu] V. I. Gurariǐ, On openings and inclinations of subspaces of a Banach space, Teor. Funktsiǐ Funktsional. Anal. i Prilozhen. 1 (1965), 194-204 (in Russian).
  • [HW] R. Herman and R. Whitley, An example concerning reflexivity, Studia Math. 28 (1967), 289-294.
  • [JR] W. B. Johnson and H. P. Rosenthal, On w*-basic sequences and their applications to the study of Banach spaces, ibid. 43 (1972), 77-92.
  • [LT] J. Lindenstrauss and L. Tzafriri, Classical Banach Spaces I. Sequence Spaces, Springer, Berlin 1977.
  • [Ma] S. Mazurkiewicz, Sur la dérivée faible d'un ensemble de fonctionnelles linéaires, Studia Math. 2 (1930), 68-71.
  • [Mc] O. C. McGehee, A proof of a statement of Banach about the weak* topology, Michigan Math. J. 15 (1968), 135-140.
  • [MM1] G. Metafune and V. B. Moscatelli, Generalized prequojections and bounded maps, Results in Math. 15 (1989), 172-178.
  • [MM2] G. Metafune and V. B. Moscatelli, Quojections and prequojections, in: Advances in the Theory of Fréchet Spaces, T. Terzioğlu (ed.), Kluwer, Dordrecht 1989, 235-254.
  • [M1] V. B. Moscatelli, On strongly non-norming subspaces, Note Mat. 7 (1987), 311-314.
  • [M2] V. B. Moscatelli, Strongly nonnorming subspaces and prequojections, Studia Math. 95 (1990), 249-254.
  • [O1] M. I. Ostrovskiǐ, w*-derived sets of transfinite order of subspaces of dual Banach spaces, Dokl. Akad. Nauk Ukrain. SSR Ser. A 1987 (10), 9-12 (in Russian).
  • [O2] M. I. Ostrovskiǐ, On total nonnorming subspaces of a conjugate Banach space, Teor. Funktsiǐ Funktsional. Anal. i Prilozhen. 53 (1990), 119-123 (in Russian); English transl.: J. Soviet Math. 58 (6) (1992), 577-579.
  • [O3] M. I. Ostrovskiǐ, Regularizability of superpositions of inverse linear operators, Teor. Funktsiǐ Funktsional. Anal. i Prilozhen. 55 (1991), 96-100 (in Russian); English transl.: J. Soviet Math. 59 (1) (1992), 652-655.
  • [Pe] A. Pełczyński, Banach spaces on which every unconditionally converging operator is weakly compact, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 10 (1962), 641-648.
  • [P] Yu. I. Petunin, Conjugate Banach spaces containing subspaces of zero characteristic, Dokl. Akad. Nauk SSSR 154 (1964), 527-529 (in Russian); English transl.: Soviet Math. Dokl. 5 (1964), 131-133.
  • [PP] Yu. I. Petunin and A. N. Plichko, The Theory of Characteristic of Subspaces and its Applications, Vishcha Shkola, Kiev 1980 (in Russian).
  • [Pl] A. N. Plichko, On bounded biorthogonal systems in some function spaces, Studia Math. 84 (1986), 25-37.
  • [S1] D. Sarason, On the order of a simply connected domain, Michigan Math. J. 15 (1968), 129-133.
  • [S2] D. Sarason, A remark on the weak-star topology of $l^∞$, Studia Math. 30 (1968), 355-359.
  • [Sc] J. J. Schäffer, Linear differential equations and functional analysis. VI, Math. Ann. 145 (1962), 354-400.
  • [W] P. Wojtaszczyk, Banach Spaces for Analysts, Cambridge Stud. Adv. Math. 25, Cambridge University Press, 1991.
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