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2011 | 31 | 2 | 231-247
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Weak compactness in the space of operator valued measures $M_ba(危,饾摏(X,Y))$ and its applications

Autorzy
Tre艣膰 / Zawarto艣膰
Warianty tytu艂u
J臋zyki publikacji
EN
Abstrakty
EN
In this note we present necessary and sufficient conditions characterizing conditionally weakly compact sets in the space of (bounded linear) operator valued measures $M_{ba}(危,饾摏(X,Y))$. This generalizes a recent result of the author characterizing conditionally weakly compact subsets of the space of nuclear operator valued measures $M_{ba}(危,饾摏鈧(X,Y))$. This result has interesting applications in optimization and control theory as illustrated by several examples.
Tw贸rcy
autor
  • EECS, University of Ottawa, Ottawa, Canada
Bibliografia
  • [1] J. Diestel and J.J. Uhl Jr, Vector Measures, American Mathematical Society, Providence, Rhode Island, 1977.
  • [2] N. Dunford and J.T. Schwartz, Linear Operators, Part 1, General Theory, Second Printing, 1964.
  • [3] J.K. Brooks, Weak compactness in the space of vector measures, Bulletin of the American Mathematical Society 78 (2) (1972), 284-287. doi: 10.1090/S0002-9904-1972-12960-4
  • [4] T. Kuo, Weak convergence of vector measures on F-spaces, Math. Z. 143 (1975), 175-180. doi: 10.7151/dmdico.1136
  • [5] I. Dobrakov, On integration in Banach spaces I, Czechoslov Math. J. 20 (95) (1970), 511-536.
  • [6] I. Dobrakov, On integration in Banach spaces IV, Czechoslov Math. J. 30 (105) (1980), 259-279.
  • [7] J.K. Brooks and P.W. Lewis, Linear operators and vector measures, Trans. American Math. Soc. 192 (1974), 139-162. doi: 10.1090/S0002-9947-1974-0338821-5
  • [8] N.U. Ahmed, Vector and operator valued measures as controls for infinite dimensional systems: optimal control Diff. Incl., Control and Optim. 28 (2008), 95-131.
  • [9] N.U. Ahmed, Impulsive perturbation of C鈧-semigroups by operator valued measures, Nonlinear Funct. Anal. & Appl. 9 (1) (2004), 127-147.
  • [10] N.U. Ahmed, Weak compactness in the space of operator valued measures, Publicationes Mathematicae, Debrechen, (PMD) 77 (3-4) (2010), 399-413.
  • [11] N.U. Ahmed, Some remarks on the dynamics of impulsive systems in Banach spaces, dynamics of continuous, Discrete and Impulsive Systems 8 (2001), 261-274.
Typ dokumentu
Bibliografia
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Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1136
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