ArticleOriginal scientific text
Title
Compactness properties of vector-valued integration maps in locally convex spaces
Authors 1, 2
Affiliations
- Mathematics Department, University of Tasmania, Hobart, Tasmania 7001, Australia
- School of Mathematics, University of New South Wales, P.O. Box 1, Kensington, New South Wales 2033, Australia
Keywords
vector measure, projective limit, weakly compact map, integration map, locally convex space
Bibliography
- C. D. Aliprantis and O. Burkinshaw, Positive Operators, Academic Press, New York, 1985.
- W. J. Davis, T. Figiel, W. B. Johnson and A. Pełczyński, Factoring weakly compact operators, J. Funct. Anal. 17 (1974), 311-327.
- J. Diestel and J. J. Uhl, Jr., Vector Measures, Math. Surveys 15, Amer. Math. Soc., Providence, 1977.
- J. Diestel and J. J. Uhl, Progress in vector measures -- 1977-83, in: Measure Theory and its Applications (Proc. Conf. Sherbrooke, Canada, 1982), Lecture Notes in Math. 1033, Springer, Berlin, 1983, 144-192.
- P. G. Dodds and W. J. Ricker, Spectral measures and the Bade reflexivity theorem, J. Funct. Anal. 61 (1985), 136-163.
- N. Dunford and J. T. Schwartz, Linear Operators, Part III: Spectral Operators, Wiley-Interscience, New York, 1972.
- I. Kluvánek, Applications of vector measures, in: Contemp. Math. 2, Amer. Math. Soc., 1980, 101-134.
- I. Kluvánek and G. Knowles, Vector Measures and Control Systems, NorthHolland, Amsterdam, 1976.
- G. Köthe, Topological Vector Spaces I, Springer, Berlin, 1969.
- D. R. Lewis, Integration with respect to vector measures, Pacific J. Math. 33 (1970), 157-165.
- S. Okada and W. Ricker, Compactness properties of the integration map associated with a vector measure, Colloq. Math. 66 (1994), 175-185.
- H. H. Schaefer, Topological Vector Spaces, Springer, New York, 1970.
- E. Thomas, The Lebesgue-Nikodym theorem for vector-valued Radon measures, Mem. Amer. Math. Soc. 139 (1974).