Cembranos Diaz, Pilar (1984) The Hereditary Dunford-Pettis Property On C(K,E). Illinois Journal of Mathematics, 91 (4). pp. 556-558. ISSN 0019-2082
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The author studies the hereditary Dunford-Pettis property for spaces CX(K) of continuous Xvalued functions (X a Banach space) on a compact Hausdorff space K. First, she shows that CX(K) has the hereditary Dunford-Pettis property if and only if one of the following holds: (a) K is finite andX has the hereditary Dunford-Pettis property; (b) C(K) and c0(X) have the hereditary Dunford-Pettis property. Unwilling to give up here, the author provides an elegant characterization of when c0(X) has the hereditary Dunford-Pettis property. Since the paper was written, Nunez has provided an elegant example (based on work of Talagrand) of an X such that, while X is hereditarily Dunford-Pettis, c0(X) is not. Remarkable and satisfying!
|Uncontrolled Keywords:||Mathematics; Applied; Mathematics|
|Subjects:||Sciences > Mathematics > Functional analysis and Operator theory|
l.C. Bessaga and A. Pelczynski, On bases and unconditional convergence of series in Banach spaces,Studia Math. 17 (1958),151-164
2. P. C. Curtis, Jr., A note concerning certain product spaces, Arch. Math. 11 (1960),50-52.
3. J. Diestel and J. J. Uhl, Vector measures, Math. Surveys,no.15,Amer.Math.Soc,Providence,R.I.,1977.
4. S. S. Khurana, Grothendieck spaces,Illinois J.Math.22 (1978),79-80.
5. J. Lindenstrauss and L. Tzafriri,Classical Banach spaces. I, Sequence spaces,vol.92,6. A.Nissen Springer-Verlag, Berlin and New York,1977.zweign, w*-sequential convergence, Israel J. Math. 22(1975),266-272.
7. A. Pelczynski, Banach spaces on which every unconditionally converging operator is weakly compact, Bull. Acad. Polon. Sei. Sér. Sei. Math. Astronom. Phys.10 (1962),641-648.
8. E. Saab and P. Saab, A stability property of a class of Banach spaces not containing a complemented copy ofh, Proc. Amer. Math. Soc. 84 (1982),44-46.
9. A. Sobczyk, Projections of the space (m) on its subspace (co), Bull. Amer. Math. Soc. 47 (1941),938-947.
|Deposited On:||24 Apr 2012 10:39|
|Last Modified:||06 Feb 2014 10:12|
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