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A separable space
with no Schauder decomposition


Authors: G. Allexandrov, Denka Kutzarova and A. Plichko
Journal: Proc. Amer. Math. Soc. 127 (1999), 2805-2806
MSC (1991): Primary 46B15
DOI: https://doi.org/10.1090/S0002-9939-99-05370-8
Published electronically: May 20, 1999
MathSciNet review: 1670410
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Abstract | References | Similar Articles | Additional Information

Abstract: We combine some known results to remark that there exists a separable Banach space which fails to have a Schauder decomposition. It can be chosen as a subspace of Gowers-Maurey space without any unconditional basic sequence.


References [Enhancements On Off] (What's this?)

  • [AD] S. Argyros and I. Deliyanni, Examples of asymptotic $\ell _1$ spaces, Trans. Amer. Math. Soc. 349 (1997), 973-995. MR 97f:46021
  • [ADKM] S. Argyros, I. Deliyanni, D. Kutzarova and A. Manousakis, Modified mixed Tsirelson spaces, J. Funct. Anal. 159 (1998), 43-109. CMP 99:04
  • [GM] W. T. Gowers and B. Maurey, The unconditional basic sequence problem, J. Amer. Math. Soc. 6 (1993), 851-874. MR 94k:46021
  • [F] V. Ferenczi, A uniformly convex hereditarily indecomposable Banach space, Israel J. Math. 102 (1997), 199-225. MR 98m:46013
  • [LT1] J. Lindenstrauss and L. Tzafriri, Classical Banach spaces I, Sequence Spaces, Springer-Verlag, 1977. MR 58:17766
  • [LT2] J. Lindenstrauss and L. Tzafriri, Classical Banach spaces II, Function Spaces, Springer-Verlag, 1979. MR 81c:46001
  • [R] J. R. Retherford, Some remarks on Schauder bases II, Rev. Rouman. Math. Pure et Appl. 13 (1968), 521-527. MR 38:4969
  • [S] Th. Schlumprecht, An arbitrarily distortable Banach space, Israel J. Math. 76 (1991), 81-95. MR 93h:46023
  • [Si] I. Singer, Bases in Banach spaces II, Springer-Verlag, 1981. MR 82k:46024

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Additional Information

G. Allexandrov
Affiliation: Department of Mathematics and Informatics, University of Sofia, Bulgaria

Denka Kutzarova
Affiliation: Institute of Mathematics, Bulgarian Academy of Sciences, Bulgaria
Address at time of publication: Department of Mathematics, University of South Carolina, Columbia, South Carolina 29208

A. Plichko
Affiliation: Department of Mathematics, Pedagogical University, Kirovograd, Ukraine

DOI: https://doi.org/10.1090/S0002-9939-99-05370-8
Received by editor(s): November 9, 1998
Published electronically: May 20, 1999
Additional Notes: The authors were partially supported by the Bulgarian Ministry of Education and Science under contract MM 506/95
Communicated by: Dale Alspach
Article copyright: © Copyright 1999 American Mathematical Society

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