Locally Asplund spaces of holomorphic functions
Christopher Boyd, Seán Dineen, and Pilar Rueda
Source: Michigan Math. J. Volume 50, Issue 3
(2002), 493-506.
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Permanent link to this document: http://projecteuclid.org/euclid.mmj/1039029979
Mathematical Reviews number (MathSciNet): MR2766
Digital Object Identifier: doi:10.1307/mmj/1039029979
References
R. Alencar, On reflexivity and basis for $\Cal P(^mE),$ Proc. Roy. Irish Acad. Sect. A 85 (1985), 131--138.
Mathematical Reviews (MathSciNet): MR845536
R. M. Aron and S. Dineen, $Q$-reflexive Banach spaces, Rocky Mountain J. Math. 27 (1997), 1009--1025.
Mathematical Reviews (MathSciNet): MR1627646
R. M. Aron, C. Hervés, and M. Valdivia, Weakly continuous mappings on Banach spaces, J. Funct. Anal. 52 (1983), 189--204.
Mathematical Reviews (MathSciNet): MR707203
Digital Object Identifier: doi:10.1016/0022-1236(83)90081-2
R. M. Aron and J. B. Prolla, Polynomial approximation of differentiable functions on Banach spaces, J. Reine Angew. Math. 313 (1980), 195--216.
Mathematical Reviews (MathSciNet): MR552473
I. A. Berezanskiĭ, Inductively reflexive locally convex spaces, Dokl. Akad. Nauk SSSR 182 (1968), 20--22.
Mathematical Reviews (MathSciNet): MR240587
C. Boyd, Distinguished preduals of spaces of holomorphic functions, Rev. Mat. Univ. Complut. Madrid 6 (1993), 221--231.
Mathematical Reviews (MathSciNet): MR1269753
------, Duality and reflexivity of spaces of approximable polynomials on locally convex spaces, Monatsh. Math. 130 (2000), 177--188.
Mathematical Reviews (MathSciNet): MR1777093
------, Preduals of spaces of vector-valued holomorphic functions, Czechoslovak Math. J. (to appear).
Mathematical Reviews (MathSciNet): MR1983458
Digital Object Identifier: doi:10.1023/A:1026287320596
C. Boyd, S. Dineen, and P. Rueda, Weakly uniformly continuous holomorphic functions and the approximation property, Indag. Math. (N.S.) 12 (2001), 147--156.
Mathematical Reviews (MathSciNet): MR1913638
Digital Object Identifier: doi:10.1016/S0019-3577(01)80022-7
H. S. Collins and W. Ruess, Duals of spaces of compact operators, Studia Math. 74 (1982), 213--245.
Mathematical Reviews (MathSciNet): MR683747
------, Weak compactness in spaces of compact operators and of vector-valued functions, Pacific J. Math. 106 (1983), 45--71.
Mathematical Reviews (MathSciNet): MR694671
A. Defant, The local Radon Nikodým property for duals of locally convex spaces, Bull. Soc. Roy. Sci. Liège 53 (1984), 233--246.
Mathematical Reviews (MathSciNet): MR770089
------, A duality theorem for locally convex tensor products, Math. Z. 190 (1985), 45--53.
Mathematical Reviews (MathSciNet): MR793347
Digital Object Identifier: doi:10.1007/BF01159162
A. Defant and K. Floret, Topological tensor products and the approximation property of locally convex spaces, Bull. Soc. Roy. Sci. Liège 58 (1989), 29--51.
Mathematical Reviews (MathSciNet): MR994895
J. Diestel and J. J. Uhl, Vector measures, Math. Surveys Monogr., 15, Amer. Math. Soc., Providence, RI, 1977.
Mathematical Reviews (MathSciNet): MR453964
Zentralblatt MATH: 0369.46039
S. Dineen, Quasi-normable spaces of holomorphic functions, Note Mat. 13 (1993), 155--195.
Mathematical Reviews (MathSciNet): MR1283528
------, Complex analysis on infinite dimensional spaces, Monogr. Math., Springer-Verlag, Berlin, 1999.
Zentralblatt MATH: 1034.46504
S. Dineen and J. Isidro, On some topological properties of the algebra of holomorphic functions, unpublished manuscript.
P. Galindo, M. Maestre, and P. Rueda, Biduality in spaces of holomorphic functions, Math. Scand. 86 (2000), 5--16.
Mathematical Reviews (MathSciNet): MR1738512
M. González and J. M. Gutiérrez, Factorization of weakly continuous holomorphic mappings, Studia Math. 118 (1996), 117--133.
Mathematical Reviews (MathSciNet): MR1389759
A. Grothendieck, Produits tensoriels topologiques et espaces nucléaries, Mem. Amer. Math. Soc. 16 (1955).
Mathematical Reviews (MathSciNet): MR75539
J. A. Jaramillo and L. A. Moraes, Duality and reflexivity in spaces of polynomials, Arch. Math. (Basel) 74 (2000), 282--293.
Mathematical Reviews (MathSciNet): MR1742640
Digital Object Identifier: doi:10.1007/s000130050444
H. Jarchow, Locally convex spaces, Teubner, Stuttgart, 1981.
Mathematical Reviews (MathSciNet): MR632257
Zentralblatt MATH: 0466.46001
J. Mujica and L. Nachbin, Linearization of holomorphic mappings on locally convex spaces, J. Math. Pures Appl. 71 (1992), 543--560.
Mathematical Reviews (MathSciNet): MR1193608
W. M. Ruess and C. P. Stegall, Extreme points in duals of operator spaces, Math. Ann. 261 (1982), 535--546.
Mathematical Reviews (MathSciNet): MR682665
Digital Object Identifier: doi:10.1007/BF01457455
C. Samuel, Reproductibilité de $\ell_1$ dans les produits tensoriels, Math. Scand. 50 (1982), 248--250.
Mathematical Reviews (MathSciNet): MR672927
L. Schwartz, Espaces de fonctions différentiables á values vectorielles, J. Anal. Math. 4 (1954/55), 88--148.
Mathematical Reviews (MathSciNet): MR80268
------, Théorie des distributions á values vectorielles I, Ann. Inst. Fourier (Grenoble) 7 (1957), 1--141.
Mathematical Reviews (MathSciNet): MR107812
M. Valdivia, Banach spaces of polynomials without copies of $\ell^1,$ Proc. Amer. Math. Soc. 123 (1995), 3143--3150.
Mathematical Reviews (MathSciNet): MR1273528
Digital Object Identifier: doi:10.2307/2160673
------, Some properties in spaces of multilinear functionals and spaces of polynomials, Proc. Roy. Irish Acad. Sect. A 98 (1998), 87--106.
Mathematical Reviews (MathSciNet): MR1760210
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