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A simple proof of the Grothendieck theorem on the Dieudonné property of $C_0(T)$


Author: T. V. Panchapagesan
Journal: Proc. Amer. Math. Soc. 129 (2001), 823-831
MSC (1991): Primary 47B38, 46G10; Secondary 28B05
DOI: https://doi.org/10.1090/S0002-9939-00-05612-4
Published electronically: September 20, 2000
MathSciNet review: 1707021
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Abstract:

Let $T$ be a locally compact Hausdorff space and let $C_0(T)$ be the Banach space of all complex valued continuous functions vanishing at infinity in $T$, provided with the supremum norm. Let $X$ be a locally convex Hausdorff space (briefly, an lcHs) which is quasicomplete. A simple proof of the Grothendieck theorem on the Dieudonné property of $C_0(T)$ is given. The present proof is much simpler than that given in an earlier work of the author (Characterizations of weakly compact operators on $C_0(T)$, Trans. Amer. Math. Soc. 350 (1998), 4849-4867).


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Additional Information

T. V. Panchapagesan
Affiliation: Departamento de Matemáticas, Facultad de Ciencias, Universidad de los Andes, Mérida, Venezuela
Email: panchapa@ciens.ula.ve

DOI: https://doi.org/10.1090/S0002-9939-00-05612-4
Received by editor(s): January 22, 1999
Received by editor(s) in revised form: May 24, 1999
Published electronically: September 20, 2000
Additional Notes: This research was supported by the project C-845-97-05-B of the C.D.C.H.T. of the Universidad de los Andes, Mérida, Venezuela.
Dedicated: Dedicated to the memory of Professor Ivan Dobrakov
Communicated by: Dale Alspach
Article copyright: © Copyright 2000 American Mathematical Society