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Quasi-reflexivity, weakly unconditionally convergent series and weak compactness

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Bibliography

  1. Bessaga, C., and A. Pelczynski: On bases and unconditional convergence of series in Banach spaces. Studia Math.18, 151–164 (1958).

    Google Scholar 

  2. —— A generalization of results of R. C. James concerning absolute bases in Banach spaces. Studia Math.18, 165–174 (1958).

    Google Scholar 

  3. Civin, P., and B. Yood: Quasi-reflexive spaces. Proc. Amer. Math. Soc.8, 906–911 (1957).

    Google Scholar 

  4. De Vito, C. L.: A completeness theorem for locally convex spaces and some applications. Math. Ann.177, 221–229 (1968).

    Google Scholar 

  5. Dixmier, J.: Sur un théorème de Banach. Duke Math. J.15, 1057–1071 (1948).

    Google Scholar 

  6. Dunford, N., and J. T. Schwartz: Linear operators, Part 1. New York: Interscience Publ. Inc. 1958.

    Google Scholar 

  7. Fleming,R. J.: Characterizations of semi-reflexivity and quasi-reflexivity. Duke Math. J. 73–81 (1969).

  8. James, R. C.: Bases and reflexivity of Banach spaces. Ann. of Math.52, 518–527 (1950).

    Google Scholar 

  9. Karlin, S.: Bases in Banach spaces. Duke Math. J.15, 971–985 (1948).

    Google Scholar 

  10. Pelczynski, A.: Banach spaces on which every unconditionally converging operator is weakly compact. Bull. Acad. Pol. Sci10, 641–648 (1962).

    Google Scholar 

  11. —— A connection between weakly unconditional convergence and weakly completeness of Banach spaces. Bull. Acad. Pol. Sci.6, 251–253 (1958).

    Google Scholar 

  12. Retherford, J. R.: Quasi-reflexivity and weakly unconditionally convergent series. Math. Ann.172, 135–138 (1967).

    Google Scholar 

  13. Schaefer, H. H.: Topological vector spaces. New York: Mac Millian and Co. 1966.

    Google Scholar 

  14. Singer, I.: On Banach spaces reflexive with respect to a linear subspace of their conjugate space III. Rev. Math. Pures et Appl.8, 139–156 (1963).

    Google Scholar 

  15. —— Weak compactness, pseudo reflexivity and quasi-reflexivity. Math. Ann.154, 77–87 (1964).

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Louisiana State University, 70802, Baton Rouge, Louisiana, USA

    J. R. Retherford

  2. Department of Mathematics, University of Missouri, Columbia, Missouri, USA

    R. J. Fleming

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  1. J. R. Retherford
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  2. R. J. Fleming
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Retherford, J.R., Fleming, R.J. Quasi-reflexivity, weakly unconditionally convergent series and weak compactness. Math. Ann. 182, 45–54 (1969). https://doi.org/10.1007/BF01350162

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