The boundary problem for L1-preduals
Jiří Spurný
Source: Illinois J. Math. Volume 52, Number 4
(2008), 1183-1193.
Abstract
Let E be an L1-predual and B⊂BE* be a boundary. We show that any bounded σ(E, B)-compact subset of E is weakly compact. We also present an example of an L1-predual E that is not angelic in the σ(E, ext BE*)-topology.
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References
E. M. Alfsen, Compact convex sets and boundary integrals, Springer-Verlag, New York, 1971.
Mathematical Reviews (MathSciNet): MR0445271
Zentralblatt MATH: 0209.42601
L. Asimow and A. J. Ellis, Convexity theory and its applications in functional analysis, Academic Press, London, 1980.
Mathematical Reviews (MathSciNet): MR0623459
Zentralblatt MATH: 0453.46013
J. Bourgain and M. Talagrand, Compacité extrémale, Proc. Amer. Math. Soc. 80 (1980), 68--70.
Mathematical Reviews (MathSciNet): MR0574510
Digital Object Identifier: doi:10.2307/2042147
JSTOR: links.jstor.org
B. Cascales and G. Godefroy, Angelicity and the boundary problem, Mathematika 45 (1998), 105--112.
Mathematical Reviews (MathSciNet): MR1644346
B. Cascales, G. Manjabacas and G. Vera, A Krein--Šmulian type result in Banach spaces, Quart. J. Math. Oxford Ser. (2) 48 (1997), 161--167.
Mathematical Reviews (MathSciNet): MR1458576
Zentralblatt MATH: 0886.46014
Digital Object Identifier: doi:10.1093/qmath/48.2.161
B. Cascales and R. Shvydkoy, On the Krein--Šmulian theorem for weaker topologies, Illinois J. Math. 47 (2003), 957--976.
Mathematical Reviews (MathSciNet): MR2036985
Zentralblatt MATH: 1040.46009
Project Euclid: euclid.ijm/1258138086
B. Cascales and G. Vera, Topologies weaker than the weak topology of a Banach space, J. Math. Anal. Appl. 182 (1994), 41--68.
Mathematical Reviews (MathSciNet): MR1265882
Zentralblatt MATH: 0808.46021
Digital Object Identifier: doi:10.1006/jmaa.1994.1066
R. Engelking, General topology, Heldermann, Berlin, 1989.
Mathematical Reviews (MathSciNet): MR1039321
M. Fabian, P. Habala, P. Hájek, V. Montesinos, J. Pelant and V. Zizler, Functional analysis and infinite-dimensional geometry, CMS books in mathematics/Ouvrages de Mathmatiques de la SMC, vol. 8, Springer-Verlag, New York, 2001.
Mathematical Reviews (MathSciNet): MR1831176
Zentralblatt MATH: 0981.46001
K. Floret, Weakly compact sets, Lectures held at S.U.N.Y., Buffalo, in Spring 1978, Lecture Notes in Mathematics, vol. 801, Springer, Berlin, 1980.
Mathematical Reviews (MathSciNet): MR0576235
Zentralblatt MATH: 0437.46006
V. P. Fonf, J. Lindenstrauss and R. R. Phelps, Infinite dimensional convexity, Handbook of the geometry of Banach spaces, vol. I, North-Holland, Amsterdam, 2001, pp. 599--670.
Mathematical Reviews (MathSciNet): MR1863703
Digital Object Identifier: doi:10.1016/S1874-5849(01)80017-6
Zentralblatt MATH: 1086.46004
D. H. Fremlin, Topological measure spaces, Torres Fremlin, England, 2003.
Mathematical Reviews (MathSciNet): MR2462372
Zentralblatt MATH: 1166.28001
G. Godefroy, Boundaries of a convex set and interpolation sets, Math. Ann. 277 (1987), 173--184.
Mathematical Reviews (MathSciNet): MR0886417
Zentralblatt MATH: 0597.46015
Digital Object Identifier: doi:10.1007/BF01457357
S. S. Khurana, Pointwise compactness on extreme points, Proc. Amer. Math. Soc. 83 (1981), 347--348.
Mathematical Reviews (MathSciNet): MR0624928
Zentralblatt MATH: 0467.46014
Digital Object Identifier: doi:10.2307/2043525
H. E. Lacey, The isometric theory of classical Banach spaces, Die Grundlehren der mathematischen Wissenschaften, vol. 208, Springer-Verlag, New York--Heidelberg, 1974.
Mathematical Reviews (MathSciNet): MR0493279
Zentralblatt MATH: 0285.46024
A. Lazar and J. Lindenstrauss, Banach spaces whose duals are $L_1$ spaces and their representing matrices, Acta Math. 126 (1971), 165--193.
Mathematical Reviews (MathSciNet): MR0291771
Zentralblatt MATH: 0209.43201
Digital Object Identifier: doi:10.1007/BF02392030
W. B. Moors and E. A. Reznichenko, Separable subspaces of affine function spaces on convex compact sets, to appear in Topology Appl., available at http://www.math.auckland.ac.nz/Research/Reports/.
Mathematical Reviews (MathSciNet): MR2423968
Zentralblatt MATH: 1155.46003
Digital Object Identifier: doi:10.1016/j.topol.2008.03.015
S. Simons, A convergence theorem with boundary, Pacific J. Math. 40 (1972), 703--708.
Mathematical Reviews (MathSciNet): MR0312193
Zentralblatt MATH: 0237.46012
Project Euclid: euclid.pjm/1102968569
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