Pacific Journal of Mathematics

Examples of hereditarily $l^1$ Banach spaces failing the Schur property.

Parviz Azimi and James N. Hagler

Article information

Source
Pacific J. Math., Volume 122, Number 2 (1986), 287-297.

Dates
First available in Project Euclid: 8 December 2004

Permanent link to this document
https://projecteuclid.org/euclid.pjm/1102701884

Mathematical Reviews number (MathSciNet)
MR831114

Zentralblatt MATH identifier
0609.46012

Subjects
Primary: 46B20: Geometry and structure of normed linear spaces
Secondary: 46B25: Classical Banach spaces in the general theory

Citation

Azimi, Parviz; Hagler, James N. Examples of hereditarily $l^1$ Banach spaces failing the Schur property. Pacific J. Math. 122 (1986), no. 2, 287--297. https://projecteuclid.org/euclid.pjm/1102701884


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References

  • [1] P. Azimi, Two Classes of Separable Banach Spaces, Ph.D.Thesis, 1982.
  • [2] C. Bessaga and A. Pelczynski, A generalization of results of R. C. James concerning absolute basis in Banach spaces, Studia Math., 17 (1958), 165-174.
  • [3] J. Bourgain, Z1 subspaces of Banach spaces, Lecture notes, Free University of Brussels.
  • [4] M. M. Day, Normed Linear Spaces, Springer Verlag, Berlin.
  • [5] J. Hagler, A counterexample to several questions about Banach spaces, Studia Math., 60 (1977), 289-307.
  • [6] R. C. James, A non-reflexive Banach space isometric with the second conjugate, Proc. Nat. Acad. Sci.U.S.A., 37 (1951), 174-177.
  • [7] J. Lindenstrauss and L. Tzafriri, Classical Banach Spaces, Vol I Sequence Spaces, Springer Verlag, Berlin.
  • [8] B. Maurey and H. P. Rosenthal, Normalized weakly null sequences with no uncondi- tional subsequence, Studia Math., 61 (1977), 77-98.
  • [9] H. P. Rosenthal, A characterization of Banach spaces containing l, Proc. Nat. Acad. Sci. U.S.A., 71 (1974), 2411-2413.