The basic sequence problem
Kalton, N.
Studia Mathematica, Tome 113 (1995), p. 167-187 / Harvested from The Polish Digital Mathematics Library

We construct a quasi-Banach space X which contains no basic sequence.

Publié le : 1995-01-01
EUDML-ID : urn:eudml:doc:216225
@article{bwmeta1.element.bwnjournal-article-smv116i2p167bwm,
     author = {N. Kalton},
     title = {The basic sequence problem},
     journal = {Studia Mathematica},
     volume = {113},
     year = {1995},
     pages = {167-187},
     zbl = {0890.46001},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv116i2p167bwm}
}
Kalton, N. The basic sequence problem. Studia Mathematica, Tome 113 (1995) pp. 167-187. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv116i2p167bwm/

[00000] [1] S. Banach, Théorie des opérations linéaires, reprint of the original 1932 edition, Chelsea, New York, 1978.

[00001] [2] J. Bastero, q-subspaces of stable p-Banach spaces, Arch. Math. (Basel) 40 (1983), 538-544. | Zbl 0503.46015

[00002] [3] L. Drewnowski, On minimally subspace-comparable F-spaces, J. Funct. Anal. 26 (1977), 315-332. | Zbl 0366.46012

[00003] [4] L. Drewnowski, Quasi-complements in F-spaces, Studia Math. 77 (1984), 373-391. | Zbl 0552.46003

[00004] [5] P. L. Duren, B. W. Romberg and A. L. Shields, Linear functionals on Hp-spaces when 0 < p < 1, J. Reine Angew. Math. 238 (1969), 32-60.

[00005] [6] T. A. Gillespie, Factorisation in Banach function spaces, Indag. Math. 43 (1981), 287-300. | Zbl 0475.46028

[00006] [7] W. T. Gowers, A solution to Banach's hyperplane problem, Bull. London Math. Soc. 26 (1994), 532-540. | Zbl 0838.46011

[00007] [8] W. T. Gowers, A new dichotomy for Banach spaces, preprint.

[00008] [9] W. T. Gowers and B. Maurey, The unconditional basic sequence problem, J. Amer. Math. Soc. 6 (1993), 851-874. | Zbl 0827.46008

[00009] [10] J. Kąkol and P. Sorjonen, Basic sequences and the Hahn-Banach extension property, Acta Sci. Math. (Szeged) 59 (1994), 161-171. | Zbl 0818.46006

[00010] [11] N. J. Kalton, Basic sequences in F-spaces and their applications, Proc. Edinburgh Math. Soc. 19 (1974), 151-167. | Zbl 0296.46010

[00011] [12] N. J. Kalton, Compact and strictly singular operators on Orlicz spaces, Israel J. Math. 26 (1977), 126-136. | Zbl 0348.47016

[00012] [13] N. J. Kalton, The three space problem for locally bounded F-spaces, Compositio Math. 37 (1978), 243-276. | Zbl 0395.46003

[00013] [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. | Zbl 0754.46001

[00014] [15] N. J. Kalton, Differentials of complex interpolation processes for Köthe function spaces, Trans. Amer. Math. Soc. 333 (1992), 479-529 . | Zbl 0776.46033

[00015] [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.

[00016] [17] N. J. Kalton and J. H. Shapiro, Bases and basic sequences in F-spaces, Studia Math. 56 (1976), 47-61. | Zbl 0334.46008

[00017] [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. | Zbl 0111.10701

[00018] [19] G. Ya. Lozanovskiĭ, On some Banach lattices, Siberian Math. J. 10 (1969), 419-430.

[00019] [20] E. Odell and T. Schlumprecht, The distortion of Hilbert space, Geom. Funct. Anal. 3 (1993), 201-217. | Zbl 0817.46023

[00020] [21] E. Odell and T. Schlumprecht, The distortion problem, Acta Math. 173 (1994), 259-283. | Zbl 0828.46005

[00021] [22] N. T. Peck, Twisted sums and a problem of Klee, Israel J. Math. 81 (1993), 357-368. | Zbl 0799.46085

[00022] [23] N. T. Peck and H. Porta, Linear topologies which are suprema of exotic topologies, Studia Math. 47 (1973), 63-73. | Zbl 0255.46009

[00023] [24] M. L. Reese, Almost-atomic spaces, Illinois J. Math. 36 (1992), 316-324. | Zbl 0789.46005

[00024] [25] M. Ribe, Necessary convexity conditions for the Hahn-Banach theorem in metrizable spaces, Pacific J. Math. 44 (1973), 715-732. | Zbl 0258.46004

[00025] [26] M. Ribe, Examples for the nonlocally convex three space problem, Proc. Amer. Math. Soc. 73 (1979), 351-355. | Zbl 0397.46002

[00026] [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.

[00027] [28] S. Rolewicz, Metric Linear Spaces, PWN, Warszawa, 1972.

[00028] [29] J. H. Shapiro, Extension of linear functionals on F-spaces with bases, Duke Math. J. 37 (1970), 639-645. | Zbl 0205.41002

[00029] [30] S. C. Tam, The basic sequence problem for quasi-normed spaces, Arch. Math. (Basel) 62 (1994), 69-72. | Zbl 0821.46003