STRICT TOPOLOGIES AND OPERATORS ON SPACES OF VECTOR-VALUED CONTINUOUS FUNCTIONS
0
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
Let X be a completely regular Hausdorff space, and E and F be Banach spaces. Let Crc(X,E) be the Banach space of all continuous functions f : X → E such that f(X) is a relatively compact set in E. We establish an integral representation theorem for bounded linear op- erators T : Crc(X, E) → F. We characterize continuous operators from Crc(X,E), provided with the strict topologies βz(X,E) (z = σ, τ) to F, in terms of their representing operator-valued measures.
Abstract
Let X be a completely regular Hausdorff space, and E and F be Banach spaces. Let Crc(X,E) be the Banach space of all continuous functions f : X → E such that f(X) is a relatively compact set in E. We establish an integral representation theorem for bounded linear op- erators T : Crc(X, E) → F. We characterize continuous operators from Crc(X,E), provided with the strict topologies βz(X,E) (z = σ, τ) to F, in terms of their representing operator-valued measures.
참고문헌 (21)
- C. D. Aliprantis, "Positive Operators" (1985), Academic Press
- J. Aguayo, "The Dunford-Pettis property on vector-valued continuous and bounded functions", Bull. Austr. Math. Soc, 48(2), pp.303~311 (1993)
- J. Aguayo-Garrido, "Weakly compact operators and u-additive mea-sures", Ann. Math. Blaise Pascal, 7(2), pp.1~11 (2000)
- J. Batt, "Applications of the Orlicz-Pettis theorem to operator-valued measures and com-pact and weakly compact linear transformations on the space of continuous functions", Rev. Roumaine Math. Pures Appl, 14, pp.907~935 (1969)
- R. Cristescu, "Topological Vector Spaces" (1977), Noordhoff Inter. Publ.
- J. Diestel, "Vector Measures", Amer. Math. Soc., Math. Surveys, 15 (1977)
- N. Dinculeanu, "Vector Measures" (1967), Pergamon Press
- N. Dinculeanu, "Vector Integration and Stochastic Integration in Banach Spaces" (2000), John Wiley and Sons Inc
- R. E. Edwards, "Functional Analysis, Theory and Applications" (1965), Holt, Rinehart and Win-ston
- R. Fontenot, "Strict topologies for vector-valued function spaces", Canad. J. Math, 26(4), pp.841~853 (1974)
- A. Katsaras, "Continuous linear functionals on spaces of vector-valued functions", Bull. Soc. Math. Greece, 15, pp.13~19 (1974)
- A. Katsaras, "Spaces of vector measures", Trans. Amer. Math. Soc, 206, pp.313~328 (1975)
- A. Katsaras, "Locally convex topologies on spaces of continuous vector functions", Math. Nachr, 71, pp.211~226 (1976)
- A. Katsaras, "Some locally convex spaces of continuous vector-valued functions over a com-pletely regular space and their duals", Trans. Amer. Math. Soc, 216, pp.367~387 (1976)
- A. Katsaras, "Integral representation of weakly compact operators", Pacific J. Math, 56(2), pp.547~556 (1975)
- S. S. Khurana, "Topologies on spaces of vector-valued continuous functions", Trans. Amer. Math. Soc, 241, pp.195~211 (1978)
- S. S. Khurana, "Integral representation of a class of operators", J. Math. Anal. Appl, 350(1), pp.290~293 (2009)
- S. S. Khurana, "Grothendieck measures", J. London Math. Soc, 39(3), pp.481~486 (1989)
- S. S. Khurana, "Strict topology and perfect measures", Czechoslovak Math. J, 40(115)(1), pp.1~7 (1990)
- M. Nowak, "Locally solid topologies on spaces of vector-valued continuous functions", Comment. Math. Univ. Carolinae, 43(3), pp.473~483 (2002)
- R. Wheeler, "A survey of Baire measures and strict topologies", Expo. Math, 2(2), pp.97~190 (1983)