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On the modulus of cone absolutely summing operators and vector measures of bounded variation


Author: Boris Lavrič
Journal: Proc. Amer. Math. Soc. 108 (1990), 479-481
MSC: Primary 47B10; Secondary 28B05, 47B55, 47D15
DOI: https://doi.org/10.1090/S0002-9939-1990-0993756-4
MathSciNet review: 993756
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Abstract: Let $ E$ and $ F$ be Banach lattices. It is shown that if $ F$ has the Levi and the Fatou property, then the ordered Banach space $ {\mathcal{L}^l}\left( {E,F} \right)$ of cone absolutely summing operators is a Banach lattice and an order ideal of the Riesz space $ {\mathcal{L}^r}\left( {E,F} \right)$ of regular operators. The same argument yields a Jordan decomposition of $ F$-valued vector measures of bounded variation.


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

  • [1] C. D. Aliprantis and O. Burkinshaw, Locally solid Riesz spaces, Academic Press, New York, 1978. MR 0493242 (58:12271)
  • [2] J. Diestel and B. Faires, On vector measures, Trans. Amer. Math. Soc. 198 (1974), 253-271. MR 0350420 (50:2912)
  • [3] B. Faires and T. J. Morrison, The Jordan decomposition of vector-valued measures, Proc. Amer. Math. Soc. 60 (1976), 139-143. MR 0419723 (54:7741)
  • [4] H. H. Schaefer, Banach lattices and positive operators, Springer-Verlag, Berlin and New York, 1974. MR 0423039 (54:11023)
  • [5] U. Schlotterbeck, Über Klassen majorisierbarer Operatoren auf Banachverbänden, Rev. Acad. Cienc. Zaragoza 20 (1971), 585-614. MR 0320809 (47:9343)
  • [6] K. D. Schmidt, Decompositions of vector measures in Riesz spaces and Banach lattices, Proc. Edinburgh Math. Soc. (2) 29 (1986), 23-39. MR 829177 (87f:46075)
  • [7] -, On the modulus of weakly compact operators and strongly additive vector measures, Proc. Amer. Math. Soc. 102 (1988), 862-866. MR 934857 (89e:47056)
  • [8] A. C. Zaanen, Riesz spaces II, North-Holland, Amsterdam, 1983. MR 704021 (86b:46001)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1990-0993756-4
Keywords: Banach lattice, cone absolutely summing operator, vector measure
Article copyright: © Copyright 1990 American Mathematical Society

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