Compactness properties of vector-valued integration maps in locally convex spaces

S. Okada; S. Ricker

Colloquium Mathematicae (1994)

  • Volume: 67, Issue: 1, page 1-14
  • ISSN: 0010-1354

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Okada, S., and Ricker, S.. "Compactness properties of vector-valued integration maps in locally convex spaces." Colloquium Mathematicae 67.1 (1994): 1-14. <http://eudml.org/doc/210259>.

@article{Okada1994,
author = {Okada, S., Ricker, S.},
journal = {Colloquium Mathematicae},
keywords = {vector measure; projective limit; weakly compact map; integration map; locally convex space; space of all scalar-valued -integrable functions; topology of convergence in mean; compactness properties of the integration map; weakly compact},
language = {eng},
number = {1},
pages = {1-14},
title = {Compactness properties of vector-valued integration maps in locally convex spaces},
url = {http://eudml.org/doc/210259},
volume = {67},
year = {1994},
}

TY - JOUR
AU - Okada, S.
AU - Ricker, S.
TI - Compactness properties of vector-valued integration maps in locally convex spaces
JO - Colloquium Mathematicae
PY - 1994
VL - 67
IS - 1
SP - 1
EP - 14
LA - eng
KW - vector measure; projective limit; weakly compact map; integration map; locally convex space; space of all scalar-valued -integrable functions; topology of convergence in mean; compactness properties of the integration map; weakly compact
UR - http://eudml.org/doc/210259
ER -

References

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  1. [1] C. D. Aliprantis and O. Burkinshaw, Positive Operators, Academic Press, New York, 1985. 
  2. [2] W. J. Davis, T. Figiel, W. B. Johnson and A. Pełczyński, Factoring weakly compact operators, J. Funct. Anal. 17 (1974), 311-327. Zbl0306.46020
  3. [3] J. Diestel and J. J. Uhl, Jr., Vector Measures, Math. Surveys 15, Amer. Math. Soc., Providence, 1977. 
  4. [4] 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. 
  5. [5] P. G. Dodds and W. J. Ricker, Spectral measures and the Bade reflexivity theorem, J. Funct. Anal. 61 (1985), 136-163. Zbl0577.46043
  6. [6] N. Dunford and J. T. Schwartz, Linear Operators, Part III: Spectral Operators, Wiley-Interscience, New York, 1972. Zbl0128.34803
  7. [7] I. Kluvánek, Applications of vector measures, in: Contemp. Math. 2, Amer. Math. Soc., 1980, 101-134. Zbl0587.28005
  8. [8] I. Kluvánek and G. Knowles, Vector Measures and Control Systems, NorthHolland, Amsterdam, 1976. Zbl0316.46043
  9. [9] G. Köthe, Topological Vector Spaces I, Springer, Berlin, 1969. Zbl0179.17001
  10. [10] D. R. Lewis, Integration with respect to vector measures, Pacific J. Math. 33 (1970), 157-165. Zbl0195.14303
  11. [11] S. Okada and W. Ricker, Compactness properties of the integration map associated with a vector measure, Colloq. Math. 66 (1994), 175-185. Zbl0884.28008
  12. [12] H. H. Schaefer, Topological Vector Spaces, Springer, New York, 1970. 
  13. [13] E. Thomas, The Lebesgue-Nikodym theorem for vector-valued Radon measures, Mem. Amer. Math. Soc. 139 (1974). 

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