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2011 | 31 | 2 | 231-247
Tytuł artykułu

Weak compactness in the space of operator valued measures $M_ba(Σ,𝓛(X,Y))$ and its applications

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EN
In this note we present necessary and sufficient conditions characterizing conditionally weakly compact sets in the space of (bounded linear) operator valued measures $M_{ba}(Σ,𝓛(X,Y))$. This generalizes a recent result of the author characterizing conditionally weakly compact subsets of the space of nuclear operator valued measures $M_{ba}(Σ,𝓛₁(X,Y))$. This result has interesting applications in optimization and control theory as illustrated by several examples.
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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 C₀-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.
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Bibliografia
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bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1136
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