Extension of Compact Operators from DF-spaces to C(K) spaces

Fernando Garibay Bonales, Rigoberto Vera Mendoza


It is proved that every compact operator from a DF-space, closed subspace of another DF-space, into the space C(K) of continuous functions on a compact Hausdorff space K can be extended to a compact operator of the total DF-space.


Topological vector spaces; DF-spaces and C(K) the spaces

Full Text:



N. Dunford and J. Schwartz, Linear Operators, vol. I., Wiley Interscience, New York, 1957.

H. Jarchow, Locally Convex Spaces, B. G. Teubener Stuttgart, 1981.

G. Kothe, Topological Vector Spaces, vol. I., Springer Verlag, New York, 1969. http://dx.doi.org/10.1007/978-3-642-64988-2

W. B. Johnson and J. Lindenstrauss, Basic concepts in the geometry of Banach spaces. Preprint. ( 2001).

W. B. Johnson and M. Zippin, Extension of operators from weak*-closed subspaces of l1 to C(K), Studia Mathematica 117 (1) (1995), 43–45.

E. Michael, Continuous Selections I, Annals of Mathematics 63 (2) (1956), 361–382. http://dx.doi.org/10.2307/1969615

E. Michael, Some Problems, Open Problems in Topology, Elsevier, Amsterdam, 1990.

L. Narici and E. Beckenstein, Topological Vector Spaces, Marcel Dekker, Inc., New York, 1985.

Abstract Views

Metrics Loading ...

Metrics powered by PLOS ALM

Esta revista se publica bajo una licencia de Creative Commons Reconocimiento-NoComercial-SinObraDerivada 4.0 Internacional.

Universitat Politècnica de València

e-ISSN: 1989-4147   https://doi.org/10.4995/agt