Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



On the modulus of weakly compact operators and strongly additive vector measures

Author: Klaus D. Schmidt
Journal: Proc. Amer. Math. Soc. 102 (1988), 862-866
MSC: Primary 47B55; Secondary 28B15, 46G10, 47B38
MathSciNet review: 934857
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Aliprantis and Burkinshaw proved that each weakly compact operator from an AL-space into a KB-space has a weakly compact modulus. In the present paper it is shown that this is also true for weakly compact operators from a Banach lattice having an order continuous dual norm into an order complete AM-space with unit. A corresponding result is obtained for strongly additive vector measures.

References [Enhancements On Off] (What's this?)

  • [1] C. D. Aliprantis and O. Burkinshaw, On weakly compact operators on Banach lattices, Proc. Amer. Math. Soc. 83 (1981), 573-578. MR 627695 (82j:47057)
  • [2] -, Positive operators, Academic Press, New York and London, 1985. MR 809372 (87h:47086)
  • [3] J. Diestel and J. J. Uhl, Jr., Vector measures, Math. Surveys, no. 15, Amer. Math. Soc., Providence, R. I., 1977. MR 0453964 (56:12216)
  • [4] H. H. Schaefer, Banach lattices and positive operators, Springer-Verlag, Berlin and New York, 1974. MR 0423039 (54:11023)
  • [5] K. D. Schmidt, On the Jordan decomposition for vector measures, Probability in Banach Spaces IV (Oberwolfach 1982), Lecture Notes in Math., vol. 990, Springer-Verlag, Berlin and New York, 1983, pp. 198-203. MR 707518 (84k:28009)
  • [6] -, Decompositions of vector measures in Riesz spaces and Banach lattices, Proc. Edinburgh Math. Soc. 29 (1986), 23-39. MR 829177 (87f:46075)
  • [7] A. W. Wickstead, Extremal structure of cones of operators, Quart. J. Math. Oxford Ser. (2) 32 (1981), 239-253. MR 615198 (82i:47069)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 47B55, 28B15, 46G10, 47B38

Retrieve articles in all journals with MSC: 47B55, 28B15, 46G10, 47B38

Additional Information

Keywords: Banach lattices, weakly compact operators, strongly additive vector measures
Article copyright: © Copyright 1988 American Mathematical Society

American Mathematical Society