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

Authors

  • Fernando Garibay Bonales Universidad Michoacana de San Nicolás de Hidalgo
  • Rigoberto Vera Mendoza Universidad Michoacana de San Nicolás de Hidalgo

DOI:

https://doi.org/10.4995/agt.2006.1921

Keywords:

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

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.

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Author Biographies

Fernando Garibay Bonales, Universidad Michoacana de San Nicolás de Hidalgo

Facultad de Ingeniería Química

Rigoberto Vera Mendoza, Universidad Michoacana de San Nicolás de Hidalgo

Facultad de Físico-Matemáticas

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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How to Cite

[1]
F. Garibay Bonales and R. Vera Mendoza, “Extension of Compact Operators from DF-spaces to C(K) spaces”, Appl. Gen. Topol., vol. 7, no. 2, pp. 165–170, Oct. 2006.

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Section

Regular Articles