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1995 | 116 | 2 | 167-187
Tytuł artykułu

The basic sequence problem

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We construct a quasi-Banach space X which contains no basic sequence.
Słowa kluczowe
Czasopismo
Rocznik
Tom
116
Numer
2
Strony
167-187
Opis fizyczny
Daty
wydano
1995
otrzymano
1994-10-17
poprawiono
1995-04-26
Twórcy
autor
Bibliografia
  • [1] S. Banach, Théorie des opérations linéaires, reprint of the original 1932 edition, Chelsea, New York, 1978.
  • [2] J. Bastero, $ℓ_q$-subspaces of stable p-Banach spaces, Arch. Math. (Basel) 40 (1983), 538-544.
  • [3] L. Drewnowski, On minimally subspace-comparable F-spaces, J. Funct. Anal. 26 (1977), 315-332.
  • [4] L. Drewnowski, Quasi-complements in F-spaces, Studia Math. 77 (1984), 373-391.
  • [5] P. L. Duren, B. W. Romberg and A. L. Shields, Linear functionals on $H^p$-spaces when 0 < p < 1, J. Reine Angew. Math. 238 (1969), 32-60.
  • [6] T. A. Gillespie, Factorisation in Banach function spaces, Indag. Math. 43 (1981), 287-300.
  • [7] W. T. Gowers, A solution to Banach's hyperplane problem, Bull. London Math. Soc. 26 (1994), 532-540.
  • [8] W. T. Gowers, A new dichotomy for Banach spaces, preprint.
  • [9] W. T. Gowers and B. Maurey, The unconditional basic sequence problem, J. Amer. Math. Soc. 6 (1993), 851-874.
  • [10] J. Kąkol and P. Sorjonen, Basic sequences and the Hahn-Banach extension property, Acta Sci. Math. (Szeged) 59 (1994), 161-171.
  • [11] N. J. Kalton, Basic sequences in F-spaces and their applications, Proc. Edinburgh Math. Soc. 19 (1974), 151-167.
  • [12] N. J. Kalton, Compact and strictly singular operators on Orlicz spaces, Israel J. Math. 26 (1977), 126-136.
  • [13] N. J. Kalton, The three space problem for locally bounded F-spaces, Compositio Math. 37 (1978), 243-276.
  • [14] N. J. Kalton, The atomic space problem and related questions for F-spaces, in: Proc. Orlicz Memorial Conf., Univ. of Mississippi, Oxford, Mississippi, 1991.
  • [15] N. J. Kalton, Differentials of complex interpolation processes for Köthe function spaces, Trans. Amer. Math. Soc. 333 (1992), 479-529 .
  • [16] N. J. Kalton, N. T. Peck and J. W. Roberts, An F-Space Sampler, London Math. Soc. Lecture Note Ser. 89, Cambridge Univ. Press, Cambridge, 1984.
  • [17] N. J. Kalton and J. H. Shapiro, Bases and basic sequences in F-spaces, Studia Math. 56 (1976), 47-61.
  • [18] V. L. Klee, Exotic topologies for linear spaces, in: Proc. Sympos. on General Topology and its Relations to Modern Analysis and Algebra, Academic Press, 1962, 238-249.
  • [19] G. Ya. Lozanovskiĭ, On some Banach lattices, Siberian Math. J. 10 (1969), 419-430.
  • [20] E. Odell and T. Schlumprecht, The distortion of Hilbert space, Geom. Funct. Anal. 3 (1993), 201-217.
  • [21] E. Odell and T. Schlumprecht, The distortion problem, Acta Math. 173 (1994), 259-283.
  • [22] N. T. Peck, Twisted sums and a problem of Klee, Israel J. Math. 81 (1993), 357-368.
  • [23] N. T. Peck and H. Porta, Linear topologies which are suprema of exotic topologies, Studia Math. 47 (1973), 63-73.
  • [24] M. L. Reese, Almost-atomic spaces, Illinois J. Math. 36 (1992), 316-324.
  • [25] M. Ribe, Necessary convexity conditions for the Hahn-Banach theorem in metrizable spaces, Pacific J. Math. 44 (1973), 715-732.
  • [26] M. Ribe, Examples for the nonlocally convex three space problem, Proc. Amer. Math. Soc. 73 (1979), 351-355.
  • [27] J. W. Roberts, A nonlocally convex F-space with the Hahn-Banach approximation property, in: Lecture Notes in Math. 604, Springer, 1977, 76-81.
  • [28] S. Rolewicz, Metric Linear Spaces, PWN, Warszawa, 1972.
  • [29] J. H. Shapiro, Extension of linear functionals on F-spaces with bases, Duke Math. J. 37 (1970), 639-645.
  • [30] S. C. Tam, The basic sequence problem for quasi-normed spaces, Arch. Math. (Basel) 62 (1994), 69-72.
Typ dokumentu
Bibliografia
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Identyfikator YADDA
bwmeta1.element.bwnjournal-article-smv116i2p167bwm
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