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

Fernando Garibay Bonales, Rigoberto Vera Mendoza
DOI: https://doi.org/10.4995/agt.2006.1921

Abstract

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.


Keywords

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

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References

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.

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Universitat Politècnica de València

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