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    Nowak, Marian 2016. Strongly bounded operators on <mml:math altimg="si1.gif" display="inline" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd" xmlns:sa="http://www.elsevier.com/xml/common/struct-aff/dtd"><mml:msub><mml:mrow><mml:mi>C</mml:mi></mml:mrow><mml:mrow><mml:mi>r</mml:mi><mml:mi>c</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>X</mml:mi><mml:mo>,</mml:mo><mml:mi>E</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math> with the strict topology <mml:math altimg="si10.gif" display="inline" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd" xmlns:sa="http://www.elsevier.com/xml/common/struct-aff/dtd"><mml:msub><mml:mrow><mml:mi>β</mml:mi></mml:mrow><mml:mrow><mml:mi>σ</mml:mi></mml:mrow></mml:msub></mml:math>. Indagationes Mathematicae,


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    Bombal, F. and Porras, B. 1989. Strictly Singular and Strictly Cosingular Operators on C(K, E). Mathematische Nachrichten, Vol. 143, Issue. 1, p. 355.


    López, A. García 1987. Operators on locally convex spaces of vector-valued continuous functions. Bulletin of the Australian Mathematical Society, Vol. 36, Issue. 02, p. 267.


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  • Mathematical Proceedings of the Cambridge Philosophical Society, Volume 97, Issue 1
  • January 1985, pp. 137-146

Characterization of some classes of operators on spaces of vector-valued continuous functions

  • Fernando Bombal (a1) and Pilar Cembranos (a1)
  • DOI: http://dx.doi.org/10.1017/S0305004100062678
  • Published online: 24 October 2008
Abstract

Let K be a compact Hausdorff space and E, F Banach spaces. We denote by C(K, E) the Banach space of all continuous. E-valued functions defined on K, with the supremum norm. It is well known ([6], [7]) that every operator (= bounded linear operator) T from C(K, E) to F has a finitely additive representing measure m of bounded semi-variation, defined on the Borel σ-field Σ of K and with values in L(E, F″) (the space of all operators from E into the second dual of F), in such a way that

where the integral is considered in Dinculeanu's sense.

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[1]R. Arens . Extension of functions on fully normal spaces. Pacific J. Math. 2 (1952), 1122.

[2]J. Batt and E. J. Berg . Linear bounded transformations on the space of continuous functions. J. Funct. Anal. 4 (1969), 215239.

[4]J. Brooks and P. Lewis . Linear operators and vector measures. Trans. Amer. Math. Soc. 192 (1974), 139162.

[6]J. Diestel and J. J. Uhl . Vector Measures. Math. surveys, no. 15 (Amer. Math. Soc., Providence, 1977).

[10]N. Ghoussoub and P. Saab . Weak compactness in spaces of Bochner integrable functions and the Radon–Nikodym property. Pacific J. Math. 110 (1984), 6570.

[13]H. E. Lacey . The Isometric Theory of Classical Banach Spaces (Springer-Verlag, 1974).

[14]J. Lindenstrauss and L. Tzafriri . Classical Banach Spaces I (Springer-Verlag, 1977).

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  • ISSN: 0305-0041
  • EISSN: 1469-8064
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