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In this note we present sufficient conditions for the existence of Radon-Nikodym derivatives (RND) of operator valued measures with respect to scalar measures. The RND is characterized by the Bochner integral in the strong operator topology of a strongly measurable operator valued function with respect to a nonnegative finite measure. Using this result we also obtain a characterization of compact sets in the space of operator valued measures. An extension of this result is also given using the theory of Pettis integral. These results have interesting applications in the study of evolution equations on Banach spaces driven by operator valued measures as structural controls.
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참고문헌 (10)
참고문헌 신청
F. J. Fernandez / 1991 / On the Radon-Nikod´ym property for operator-valued measures / Period. Math. Hungar 22 (3) : 147 ~ 151
H. B. Maynard / 1972 / A Radon-Nikod´ym theorem for operator-valued measures / Trans. Amer. Math. Soc 173 : 449 ~ 463
I. Dobrakov / 1970 / On integration in Banach spaces I / Czechoslovak Math. J 20 (95) : 511 ~ 536
I. Dobrakov / 1980 / On Integration in Banach Spaces IV / Czechoslovak Math. J 30 (2) : 25979 ~
J. Diestel / 1977 / Vector Measures / American Mathematical Society
H. B. Maynard / 1972 / A Radon-Nikod´ym theorem for operator-valued measures / Trans. Amer. Math. Soc 173 : 449 ~ 463
I. Dobrakov / 1970 / On integration in Banach spaces I / Czechoslovak Math. J 20 (95) : 511 ~ 536
I. Dobrakov / 1980 / On Integration in Banach Spaces IV / Czechoslovak Math. J 30 (2) : 25979 ~
J. Diestel / 1977 / Vector Measures / American Mathematical Society
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