A General Construction of Spaces of the Type of R. C. James
Canadian journal of mathematics, Tome 27 (1975) no. 6, pp. 1263-1270

Voir la notice de l'article provenant de la source Cambridge University Press

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].
Lohman, Robert H.; Casazza, Peter G. A General Construction of Spaces of the Type of R. C. James. Canadian journal of mathematics, Tome 27 (1975) no. 6, pp. 1263-1270. doi: 10.4153/CJM-1975-131-3
@article{10_4153_CJM_1975_131_3,
     author = {Lohman, Robert H. and Casazza, Peter G.},
     title = {A {General} {Construction} of {Spaces} of the {Type} of {R.} {C.} {James}},
     journal = {Canadian journal of mathematics},
     pages = {1263--1270},
     year = {1975},
     volume = {27},
     number = {6},
     doi = {10.4153/CJM-1975-131-3},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1975-131-3/}
}
TY  - JOUR
AU  - Lohman, Robert H.
AU  - Casazza, Peter G.
TI  - A General Construction of Spaces of the Type of R. C. James
JO  - Canadian journal of mathematics
PY  - 1975
SP  - 1263
EP  - 1270
VL  - 27
IS  - 6
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1975-131-3/
DO  - 10.4153/CJM-1975-131-3
ID  - 10_4153_CJM_1975_131_3
ER  - 
%0 Journal Article
%A Lohman, Robert H.
%A Casazza, Peter G.
%T A General Construction of Spaces of the Type of R. C. James
%J Canadian journal of mathematics
%D 1975
%P 1263-1270
%V 27
%N 6
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1975-131-3/
%R 10.4153/CJM-1975-131-3
%F 10_4153_CJM_1975_131_3

[1] 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] 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] 3. Civin, P. and Yood, B., Qua si-reflexive spaces, Proc. Amer. Math. Soc. 9 (1957), 906–911. Google Scholar

[4] 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] 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] 6. Herman, R. and Whitley, R., An example concerning reflexivity, Studia Math. 28 (1967), 289–294. Google Scholar

[7] 7. James, R. C., Bases and reflexivity of Banach spaces, Ann. of Math. 52 (1950), 518–527. Google Scholar

[8] 8. James, R. C., Super-reflexive spaces with bases, Pacific J. Math. 41 (1972), 409–419. Google Scholar

[9] 9. Lindenstrauss, J., On James’ paper “Separable conjugate spaces,” Israel J. Math. 9 (1971), 279–284. Google Scholar

[10] 10. Lindenstrauss, J. and Tzafriri, L., On Orlicz sequence spaces, Israel J. Math. 10 (1971), 379–390. Google Scholar

[11] 11. Ruckle, W., On the construction of sequence spaces that have Schauder bases, Can. J. Math. 18 (1966), 1281–1293. Google Scholar

[12] 12. Singer, I., Bases and quasi-reflexivity of Banach spaces, Math. Annalen 153 (1964), 199–209. Google Scholar

[13] 13. Singer, I., Bases in Banach spaces I. (New York, Springer-Verlag, 1970). Google Scholar

[14] 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

Cité par Sources :