Publication:
Sequential convergences and Dunford-Pettis properties

Loading...
Thumbnail Image
Full text at PDC
Publication Date
2000
Advisors (or tutors)
Editors
Journal Title
Journal ISSN
Volume Title
Publisher
Suomalainen Tiedeakatemia
Citations
Google Scholar
Research Projects
Organizational Units
Journal Issue
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.
Description
Unesco subjects
Keywords
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.
Collections