|
A separable space with no Schauder decomposition
Author(s):
G.
Allexandrov;
Denka
Kutzarova;
A.
Plichko
Journal:
Proc. Amer. Math. Soc.
127
(1999),
2805-2806.
MSC (1991):
Primary 46B15
Posted:
May 20, 1999
MathSciNet review:
1670410
Retrieve article in:
PDF
This article is available free of charge
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:
- [AD]
- S. Argyros and I. Deliyanni, Examples of asymptotic
 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
Similar Articles:
Retrieve articles in Proceedings of the American Mathematical
Society
with
MSC (1991):
46B15
Retrieve articles in all Journals with
MSC (1991):
46B15
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:
10.1090/S0002-9939-99-05370-8
PII:
S 0002-9939(99)05370-8
Received by editor(s):
November 9, 1998
Posted:
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
Copyright of article:
Copyright
1999,
American Mathematical Society
|
