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A General Construction of Spaces of the Type of R. C. James

Published online by Cambridge University Press:  20 November 2018

Robert H. Lohman  and
Peter G. Casazza
Robert H. Lohman
Affiliation:
University of A labama Huntsville, Alabama
Peter G. Casazza
Affiliation:
Kent State University Kent, Ohio
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In 1950, R. C. James [7] exhibited a nonreflexive Banach space with a basis that is of finite codimension in its second dual. This space is the first example of a quasi-reflexive space. General results on quasi-reflexive spaces have been obtained by P. Civin and B. Yood [3], and quasi-reflexive spaces with bases have been studied by D. Dean, B. L. Lin, and I. Singer [4 ; 12].

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 27 , Issue 6 , 01 December 1975 , pp. 1263 - 1270
Copyright
Copyright © Canadian Mathematical Society 1975

References

1. Altschuler, Z., Casazza, P. G. and Lin, B. L., On symmetric basic sequences in Lorentz sequence spaces, Israel J. Math. 15 (1973), 140–155.Google Scholar
2. Casazza, P. G. and Lin, B. L., On symmetric basic sequences in Lorentz sequence spaces II, Israel J. Math. 17 (1974), 191–218.Google Scholar
3. Civin, P. and Yood, B., Qua si-reflexive spaces, Proc. Amer. Math. Soc. 9 (1957), 906–911.Google Scholar
4. Dean, D. W., Lin, B. L. and Singer, I., On k-shrinking and k-boundedly complete bases in Banach spaces, Pacific J. Math. 32 (1970), 323–331.Google Scholar
5. Dubinsky, E., Pelczynski, A. and Rosenthal, H. P., On Banach spaces X for which ir2 (J*,, X) = B﹛<£ X), Studia Math. U (1972), 617–648.Google Scholar
6. Herman, R. and Whitley, R., An example concerning reflexivity, Studia Math. 28 (1967), 289–294.Google Scholar
7. James, R. C., Bases and reflexivity of Banach spaces, Ann. of Math. 52 (1950), 518–527.Google Scholar
8. James, R. C., Super-reflexive spaces with bases, Pacific J. Math. 41 (1972), 409–419.Google Scholar
9. Lindenstrauss, J., On James’ paper “Separable conjugate spaces,” Israel J. Math. 9 (1971), 279–284.Google Scholar
10. Lindenstrauss, J. and Tzafriri, L., On Orlicz sequence spaces, Israel J. Math. 10 (1971), 379–390.Google Scholar
11. Ruckle, W., On the construction of sequence spaces that have Schauder bases, Can. J. Math. 18 (1966), 1281–1293.Google Scholar
12. Singer, I., Bases and quasi-reflexivity of Banach spaces, Math. Annalen 153 (1964), 199–209.Google Scholar
13. Singer, I., Bases in Banach spaces I. (New York, Springer-Verlag, 1970).Google Scholar
14. Sternbach, L., On k-shrinking and k-boundedly complete basic sequences and quasi-reflexive spaces, Pacific J. Math. 37 (1971), 817–824.Google Scholar