Publication: Sequential convergences and Dunford-Pettis properties
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Publication Date
2000
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Suomalainen Tiedeakatemia
Abstract
Several forms of the Dunford-Pettis property are studied, each related to a different mode of sequential convergence, and a different class of weakly compact functions. The relationship between these Dunford-Pettis properties is investigated, and the appearance of previously studied Dunford-Pettis properties is pointed out, giving a unifying approach to the subject.
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Análisis funcional y teoría de operadores
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Citation
Aron, R.M., Y.S. Choi, and J.G. Llavona: Estimates by polynomials. - Bull. Austral. Math. Soc. 52, 1995, 475-486.
Biström, P., J.A. Jaramillo, and M. Lindström: Polynomial compactness in Banach spaces. - Rocky Mountain J. Math. 28(1), 1998, 1203-1226.
Borwein, J., M. Fabian, and J. Vanderwerff: Characterizations of Banach spaces via convex and other locally Lipschitz functions. - Acta Math. Vietnam. 22(1), 1997, 53-69.
Bourgain, J.: H1 is a Grothendieck space. - Studia Math. 75, 1982, 193-226.
Bourgain, J.: New Banach space properties of the disc algebra and H1. - Acta Math.152, 1984, 1-48.
Castillo, J.M.F., and F. Sánchez: Dunford-Pettis-like properties of continuous vector function spaces. - Rev. Mat. Univ. Complut. Madrid 6(1), 1993, 43-59.
Cembranos, P.: The hereditary Dunford-Pettis property on C(K;E) . - Illinois J. Math. 31(3), 1987, 365-373.
Diestel, J.: A survey of results related to the Dunford-Pettis property. - Contemp. Math. 2, Amer. Math. Soc., Providence, RI, 1980, 15-60.
Diestel, J.: Sequences and Series in Banach Spaces. - Graduate Texts in Math. 92, Springer-Verlag, New York, 1984.
Dineen, S.: Complex Analysis on Infinite Dimensional Spaces. - Springer Monogr. Math., Springer-Verlag, London, 1999.
Dudley, R.M.: On sequential convergence. - Trans. Amer. Math. Soc. 112, 1964, 483-507.
Farmer, J.D., and W.B. Johnson: Polynomial Schur and polynomial Dunford-Pettis properties. - Contemp. Math. 144, 1993, 95-105.
Josefson, B.: Weak sequential convergence in the dual of a Banach space does not imply norm convergence. - Ark. Mat. 13, 1975, 79-89.
Pelczynski, A.: A property of multilinear operations. - Studia Math. 16, 1957, 173-182.
Petunin, Y.I., and V.I. Savkin: Convergence generated by analytic functions. – Ukranian Math. J. 40, 1988, 676-679.
Ryan, R.A.: Dunford {Pettis properties. - Bull. Acad. Polon. Sci. Math. 27, 1979, 373-379.
Ryan, R.A.: Weakly compact holomorphic mappings on Banach spaces. - Paci¯c J. Math. 131(1), 1988, 179-190.
Schaefer, H.H.: Topological Vector Spaces. - Graduate Texts in Math. 3, Springer-Verlag, New York, 1971.