Some characterizations of reflexivity

Singer, Ivan

doi:10.1090/S0002-9939-1975-0511796-8

Some characterizations of reflexivity
HTML articles powered by AMS MathViewer

by Ivan Singer PDF

Proc. Amer. Math. Soc. 52 (1975), 166-168 Request permission

Abstract:

The results of R. C. James on characterizations of reflexivity of Banach spaces with an unconditional basis in terms of ${c_0}$ and ${l^1}$ are extended to arbitrary Banach spaces. Some consequences are obtained.

References

C. Bessaga and A. Pełczyński, A generalization of results of R. C. James concerning absolute bases in Banach spaces, Studia Math. 17 (1958), 165–174. MR 115071, DOI 10.4064/sm-17-2-165-174
C. Bessaga and A. Pełczyński, On subspaces of a space with an absolute basis, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astr. Phys. 6 (1958), 313–315. MR 0096956
A. Grothendieck, Espaces vectoriels topologiques, Universidade de São Paulo, Instituto de Matemática Pura e Aplicada, São Paulo, 1954 (French). MR 0077884
Robert C. James, Bases and reflexivity of Banach spaces, Ann. of Math. (2) 52 (1950), 518–527. MR 39915, DOI 10.2307/1969430
Joram Lindenstrauss, Some aspects of the theory of Banach spaces, Advances in Math. 5 (1970), 159–180 (1970). MR 279566, DOI 10.1016/0001-8708(70)90032-0
A. Pełczyński, A connection between weakly unconditional convergence and weakly completeness of Banach spaces, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astr. Phys. 6 (1958), 251–253 (unbound insert) (English, with Russian summary). MR 0115072
A. Pełczyński, On Banach spaces containing $L_{1}(\mu )$, Studia Math. 30 (1968), 231–246. MR 232195, DOI 10.4064/sm-30-2-231-246
Haskell P. Rosenthal, A characterization of Banach spaces containing $l^{1}$, Proc. Nat. Acad. Sci. U.S.A. 71 (1974), 2411–2413. MR 358307, DOI 10.1073/pnas.71.6.2411
Ivan Singer, Bases in Banach spaces. I, Die Grundlehren der mathematischen Wissenschaften, Band 154, Springer-Verlag, New York-Berlin, 1970. MR 0298399