# A normalized weakly null sequence with no shrinking subsequence in a Banach space not containing ${\ell}_{1}$

Compositio Mathematica (1980)

- Volume: 41, Issue: 2, page 287-295
- ISSN: 0010-437X

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top## How to cite

topOdell, E.. "A normalized weakly null sequence with no shrinking subsequence in a Banach space not containing $\ell _1$." Compositio Mathematica 41.2 (1980): 287-295. <http://eudml.org/doc/89459>.

@article{Odell1980,

author = {Odell, E.},

journal = {Compositio Mathematica},

keywords = {normalized weakly null sequence with no shrinking subsequence; unconditional subsequence; block basis of constant modulus coefficient; bounded Baire class 1 function},

language = {eng},

number = {2},

pages = {287-295},

publisher = {Sijthoff et Noordhoff International Publishers},

title = {A normalized weakly null sequence with no shrinking subsequence in a Banach space not containing $\ell _1$},

url = {http://eudml.org/doc/89459},

volume = {41},

year = {1980},

}

TY - JOUR

AU - Odell, E.

TI - A normalized weakly null sequence with no shrinking subsequence in a Banach space not containing $\ell _1$

JO - Compositio Mathematica

PY - 1980

PB - Sijthoff et Noordhoff International Publishers

VL - 41

IS - 2

SP - 287

EP - 295

LA - eng

KW - normalized weakly null sequence with no shrinking subsequence; unconditional subsequence; block basis of constant modulus coefficient; bounded Baire class 1 function

UR - http://eudml.org/doc/89459

ER -

## References

top- [1] J. Bourgain: On convergent sequences of continuous functions (preprint). Zbl0474.54008MR682645
- [2] R.C. James, A separable somewhat reflexive Banach space with nonseparable dual Bull. Amer. Math. Soc.80 (1974) 738-743. Zbl0286.46018MR417763
- [3] W.B. Johnson and H.P. Rosenthal, On w*-basic sequences and their applications to the study of Banach spaces, Studia Math., 43 (1972), 77-92. Zbl0213.39301MR310598
- [4] J. Lindenstrauss and C. Stegall, Examples of separable spaces which do not contain l1 and whose duals are non-separable, Studia Math., 54 (1975), 81-105. Zbl0324.46017MR390720
- [5] B. Maurey and H.P. Rosenthal, Normalized weakly null sequences with no unconditional subsequence, Studia Math., 61 (1977), 77-98. Zbl0357.46025MR438091
- [6] E. Odell, Applications of Ramsey theorems to Banach space theory, Analysis Seminar at Texas, (to appear). Zbl0468.46009MR606226
- [7] H.P. Rosenthal, A characterization of Banach spaces continuing l1, Proc. Nat. Acad. Sci. U.S.A., 71 (1974), 2411-2413. Zbl0297.46013MR358307

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