Weakly continuous functions on Banach spaces not containing
Author:
Joaquín M. Gutiérrez
Journal:
Proc. Amer. Math. Soc. 119 (1993), 147152
MSC:
Primary 46B20; Secondary 46G99
MathSciNet review:
1158000
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Abstract 
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Abstract: Banach spaces not containing are characterized in terms of continuous and holomorphic functions and polynomials which are weakly sequentially continuous and weakly continuous on bounded subsets. An application to (bounded linear) operators is also given.
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 [1]
 R. M. Aron, Weakly uniformly continuous and weakly sequentially continuous entire functions, Advances in Holomorphy, Math. Studies, vol. 34, NorthHolland, Amsterdam, 1979, pp. 4766. MR 0632031 (58:30210)
 [2]
 R. M. Aron, B. J. Cole, and T. W. Gamelin, Spectra of algebras of analytic functions on a Banach space, J. Reine Angew. Math. 415 (1991), 5193. MR 1096902 (92f:46056)
 [3]
 R. M. Aron, J. Diestel, and A. K. Rajappa, Weakly continuous functions on Banach spaces containing , Banach Spaces (Proceedings, Missouri 1984), Lecture Notes in Math., vol. 1166, SpringerVerlag, Berlin, 1985, pp. 13. MR 827751 (87g:46022)
 [4]
 R. M. Aron and C. Hervés, Weakly sequentially continuous analytic functions on a Banach space, Functional Analysis, Holomorphy and Approximation Theory II, Math. Studies, vol. 86, NorthHolland, Amsterdam, 1984, pp. 2338. MR 771320 (86k:46072)
 [5]
 R. M. Aron, C. Hervés, and M. Valdivia, Weakly continuous mappings on Banach spaces, J. Funct. Anal. 52 (1983), 189204. MR 707203 (84g:46066)
 [6]
 R. M. Aron and J. B. Prolla, Polynomial approximation of differentiable functions on Banach spaces, J. Reine Angew. Math. 313 (1980), 195216. MR 552473 (81c:41078)
 [7]
 E. M. Bator, P. Lewis, and D. Race, Some connections between Pettis integration and operator theory, Rocky Mountain J. Math. 17 (1987), 683695. MR 923739 (89b:46060)
 [8]
 J. Diestel, Sequences and series in Banach spaces, Graduate Texts in Math., vol. 92, SpringerVerlag, Berlin, 1984. MR 737004 (85i:46020)
 [9]
 J. Ferrera, J. Gómez, and J. G. Llavona, On completion of spaces of weakly continuous functions, Bull. London Math. Soc. 15 (1983), 260264. MR 697129 (84g:46050)
 [10]
 M. González and J. M. Gutiérrez, The compact weak topology on a Banach space, Proc. Roy. Soc. Edinburgh Sect. A 120 (1992), 367379.
 [11]
 J. A. Jaramillo and J. G. Llavona, Homomorphisms between algebras of continuous functions, Canad. J. Math. 41 (1989), 132162. MR 996722 (91h:46095)
 [12]
 J. Lindenstrauss and L. Tzafriri, Classical Banach spaces, I. Sequence spaces, Ergeb. Math. Grenzgeb. (3), vol. 92, SpringerVerlag, Berlin, 1977. MR 0500056 (58:17766)
 [13]
 J. G. Llavona, Approximation of continuously differentiable functions, Math. Studies, vol. 130, NorthHolland, Amsterdam, 1986. MR 870155 (88f:41001)
 [14]
 J. Mujica, Complex analysis in Banach spaces, Math. Studies, vol. 120, NorthHolland, Amsterdam, 1986. MR 842435 (88d:46084)
 [15]
 H. P. Rosenthal, Pointwise compact subsets of the first Baire class, Amer. J. Math. 99 (1977), 362378. MR 0438113 (55:11032)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029939199311580009
PII:
S 00029939(1993)11580009
Keywords:
Space not containing ,
polynomial,
holomorphic function,
weakly sequentially continuous function
Article copyright:
© Copyright 1993 American Mathematical Society
