Coreflexive and somewhat reflexive Banach spaces
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- by James R. Clark PDF
- Proc. Amer. Math. Soc. 36 (1972), 421-427 Request permission
Abstract:
A coreflexive Banach space is shown to have many of the same properties as a quasi-reflexive space. An infinite dimensional reflexive subspace of a Banach space with boundedly complete basis and separable dual is constructed, and it is noted that somewhat reflexive Banach spaces need not be coreflexive.References
- C. Bessaga and A. Pełczyński, On bases and unconditional convergence of series in Banach spaces, Studia Math. 17 (1958), 151–164. MR 115069, DOI 10.4064/sm-17-2-151-164
- Paul Civin and Bertram Yood, Quasi-reflexive spaces, Proc. Amer. Math. Soc. 8 (1957), 906–911. MR 90020, DOI 10.1090/S0002-9939-1957-0090020-6
- William J. Davis and Ivan Singer, Boundedly complete $M$-bases and complemented subspaces in Banach spaces, Trans. Amer. Math. Soc. 175 (1973), 187–194. MR 317011, DOI 10.1090/S0002-9947-1973-0317011-5 M. M. Day, Normed linear spaces, 2nd ed., Ergebnisse der Mathematik und ihrer Grenzgebiete, N. F., Heft 21, Academic Press, New York; Springer-Verlag, Berlin, 1962. MR 26 #2847.
- J. Dixmier, Sur un théorème de Banach, Duke Math. J. 15 (1948), 1057–1071 (French). MR 27440
- Nelson Dunford and Jacob T. Schwartz, Linear Operators. I. General Theory, Pure and Applied Mathematics, Vol. 7, Interscience Publishers, Inc., New York; Interscience Publishers Ltd., London, 1958. With the assistance of W. G. Bade and R. G. Bartle. MR 0117523
- R. Herman and R. Whitley, An example concerning reflexivity, Studia Math. 28 (1966/67), 289–294. MR 215056, DOI 10.4064/sm-28-3-289-294
- Robert C. James, Separable conjugate spaces, Pacific J. Math. 10 (1960), 563–571. MR 117528
- W. B. Johnson and H. P. Rosenthal, On $\omega ^{\ast }$-basic sequences and their applications to the study of Banach spaces, Studia Math. 43 (1972), 77–92. MR 310598, DOI 10.4064/sm-43-1-77-92
- Joram Lindenstrauss, On James’s paper “Separable conjugate spaces”, Israel J. Math. 9 (1971), 279–284. MR 279567, DOI 10.1007/BF02771677
- R. D. McWilliams, On certain Banach spaces which are $w^{\ast }$-sequentially dense in their second duals, Duke Math. J. 37 (1970), 121–126. MR 259570
- A. Pełczyński, On strictly singular and strictly cosingular operators. I. Strictly singular and strictly cosingular operators in $C(S)$-spaces, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 13 (1965), 31–36. MR 177300
- Ivan Singer, Weak compactness, pseudo-reflexivity and quasi-reflexivity, Math. Ann. 154 (1964), 77–87. MR 165349, DOI 10.1007/BF01360728
- Angus E. Taylor, Introduction to functional analysis, John Wiley & Sons, Inc., New York; Chapman & Hall, Ltd., London, 1958. MR 0098966
- R. J. Whitley, Strictly singular operators and their conjugates, Trans. Amer. Math. Soc. 113 (1964), 252–261. MR 177302, DOI 10.1090/S0002-9947-1964-0177302-2
Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 36 (1972), 421-427
- MSC: Primary 46B10
- DOI: https://doi.org/10.1090/S0002-9939-1972-0308748-7
- MathSciNet review: 0308748