JOURNAL BROWSE
Search
Advanced SearchSearch Tips
A NOTE ON RADON-NIKODYM THEOREM FOR OPERATOR VALUED MEASURES AND ITS APPLICATIONS
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
A NOTE ON RADON-NIKODYM THEOREM FOR OPERATOR VALUED MEASURES AND ITS APPLICATIONS
Ahmed, Nasiruddin;
  PDF(new window)
 Abstract
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.
 Keywords
space of operator valued measures;strong operator topology;Radon-Nikodym theorem;RNP;Bochner and Pettis integrals;evolution equations on Banach spaces;
 Language
English
 Cited by
1.
Remarks on Measurability of Operator-Valued Functions, Mediterranean Journal of Mathematics, 2016, 13, 6, 5147  crossref(new windwow)
 References
1.
N. U. Ahmed, Vector and Operator Valued Measures as Controls for Infinite Dimensional Systems: Optimal Control, Discuss. Math. Differ. Incl. Control Optim. 28 (2008), 95-131. crossref(new window)

2.
J. Diestel and J. J. Uhl, Jr., Vector Measures, American Mathematical Society, Providence, R.I., 1977.

3.
I. Dobrakov, On integration in Banach spaces I, Czechoslovak Math. J. 20(95) (1970), 511-536.

4.
I. Dobrakov, On Integration in Banach Spaces IV, Czechoslovak Math. J. 30(105) (1980), no. 2, 259-79.

5.
N. Dunford and J. T. Schwartz, Linear Operators, Part 1, General Theory, Second Printing, Interscience Publishers, Inc., New York, 1964.

6.
F. J. Fernandez and P. J. Guerra, On the Radon-Nikodym property for operator-valued measures, Period. Math. Hungar. 22 (1991), no. 3, 147-151. crossref(new window)

7.
H. B. Maynard, A Radon-Nikodym theorem for operator-valued measures, Trans. Amer. Math. Soc. 173 (1972), 449-463.

8.
S. Moedomo and J. J. Uhl, Jr., Radon-Nikodym theorems for the Bochner and Pettis integrals, Pacific J. Math. 38 (1971), no. 2, 531-536. crossref(new window)

9.
T. V. Panchapagesan, On the distinguishing features of the Dobrakov integral, Divulg. Mat. 3 (1995), no. 1, 79-114.

10.
M. A. Rieffel, The Radon-Nikodym theorem for the Bochner integral, Trans. Amer. Math. Soc. 131 (1968), 466-487. crossref(new window)