On sequences spanning a complex $l_1$ space
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- by Leonard E. Dor PDF
- Proc. Amer. Math. Soc. 47 (1975), 515-516 Request permission
Abstract:
If $({f_n})$ is a bounded sequence in a complex Banach space $B$, and no subsequence of $({f_n})$ is weakly Cauchy, then a subsequence of $({f_n})$ is equivalent to the unit vector basis of the complex ${l_1}$ space.References
- Haskell P. Rosenthal, A characterization of Banach spaces containing $l^{1}$, Proc. Nat. Acad. Sci. U.S.A. 71 (1974), 2411โ2413. MR 358307, DOI 10.1073/pnas.71.6.2411
Additional Information
- © Copyright 1975 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 47 (1975), 515-516
- MSC: Primary 46B15
- DOI: https://doi.org/10.1090/S0002-9939-1975-0358308-X
- MathSciNet review: 0358308