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A note on multiplication of strong operator measurable functions


Author: G. Schlüchtermann
Journal: Proc. Amer. Math. Soc. 123 (1995), 2815-2816
MSC: Primary 46G10; Secondary 46E40, 47A56
DOI: https://doi.org/10.1090/S0002-9939-1995-1260179-7
MathSciNet review: 1260179
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Abstract: Let $ (\Omega ,\Sigma ,\mu )$ be a finite and positive measure space, and let $ {U_1}, \ldots ,{U_n}$ be strongly measurable functions with values in the space of bounded linear operators on a Banach space. Then the product $ {U_1} \cdots {U_n}$ is again strongly measurable.


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

  • [BJY] A. Badrikian, G. W. Johnson, and I. Yoo, The composition of operator-valued measurable functions is measurable, Proc. Amer. Math. Soc. (to appear). MR 1242072 (95g:28021)
  • [Din] N. Dinculeanu, Vector measures, VEB Deutscher Verlag der Wissenschaften, Berlin, 1966. MR 0206189 (34:6011a)
  • [Jo] G. W. Johnson, The product of strong operator measurable functions is strong operator measurable, Proc. Amer. Math. Soc. 117 (1993), 1097-1104. MR 1123654 (93e:46049)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1995-1260179-7
Article copyright: © Copyright 1995 American Mathematical Society

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