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A simple proof of the Grothendieck theorem on the Dieudonné property of 
Author(s):
T.
V.
Panchapagesan
Journal:
Proc. Amer. Math. Soc.
129
(2001),
823-831.
MSC (1991):
Primary 47B38, 46G10;
Secondary 28B05
Posted:
September 20, 2000
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Abstract:
Let  be a locally compact Hausdorff space and let  be the Banach space of all complex valued continuous functions vanishing at infinity in  , provided with the supremum norm. Let  be a locally convex Hausdorff space (briefly, an lcHs) which is quasicomplete. A simple proof of the Grothendieck theorem on the Dieudonné property of  is given. The present proof is much simpler than that given in an earlier work of the author (Characterizations of weakly compact operators on  , 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:
10.1090/S0002-9939-00-05612-4
PII:
S 0002-9939(00)05612-4
Received by editor(s):
January 22, 1999
Received by editor(s) in revised form:
May 24, 1999
Posted:
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
Copyright of article:
Copyright
2000,
American Mathematical Society
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