no. 2
A normalized weakly null sequence with no shrinking subsequence in a Banach space not containing ℓ 1
Compositio Mathematica, Tome 41 (1980) no. 2, pp. 287-295 
@article{CM_1980__41_2_287_0,
     author = {Odell, E.},
     title = {A normalized weakly null sequence with no shrinking subsequence in a {Banach} space not containing $\ell _1$},
     journal = {Compositio Mathematica},
     pages = {287--295},
     year = {1980},
     publisher = {Sijthoff et Noordhoff International Publishers},
     volume = {41},
     number = {2},
     mrnumber = {581585},
     zbl = {0437.46010},
     language = {en},
     url = {https://www.numdam.org/item/CM_1980__41_2_287_0/}
}
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Odell, E. A normalized weakly null sequence with no shrinking subsequence in a Banach space not containing $\ell _1$. Compositio Mathematica, Tome 41 (1980) no. 2, pp. 287-295. https://www.numdam.org/item/CM_1980__41_2_287_0/

[1] J. Bourgain: On convergent sequences of continuous functions (preprint). | Zbl | MR

[2] R.C. James, A separable somewhat reflexive Banach space with nonseparable dual Bull. Amer. Math. Soc. 80 (1974) 738-743. | Zbl | MR

[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. | Zbl | MR

[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. | Zbl | MR

[5] B. Maurey and H.P. Rosenthal, Normalized weakly null sequences with no unconditional subsequence, Studia Math., 61 (1977), 77-98. | Zbl | MR

[6] E. Odell, Applications of Ramsey theorems to Banach space theory, Analysis Seminar at Texas, (to appear). | Zbl | MR

[7] H.P. Rosenthal, A characterization of Banach spaces continuing l1, Proc. Nat. Acad. Sci. U.S.A., 71 (1974), 2411-2413. | Zbl | MR