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Proyecciones (Antofagasta)

versión impresa ISSN 0716-0917

Proyecciones (Antofagasta) v.28 n.3 Antofagasta dic. 2009

http://dx.doi.org/10.4067/S0716-09172009000300004 

Proyecciones Journal of Mathematics
Vol. 28, N° 3, pp. 233-237, December 2009.
Universidad Católica del Norte
Antofagasta - Chile


COMPACT OPERATORS


Charles Swartz


New Mexico State University, U. S. A.


Correspondencia a:


Abstract

We give a characterization in terms of the transpose operator for a continuous linear operator between locally convex spaces to map bounded sets into relatively weakly compact [relatively compact, precompact] sets. Our results give a known characterization for compact operators between Banach spaces.



References

[DS] N. Dunford and J. Schwartz, Linear Operators, Interscience, N. Y., (1957).        [ Links ]

[Ko1] G. Kothe, Topological Vector Spaces I, Springer-Verlag, Berlin, (1966).        [ Links ]

[Ko2] G. Kothe, Topological Vector Spaces II, Springer-Verlag, Berlin, (1979).        [ Links ]

[Ku] S. S. Khurana, Quasi-Mackey Topology, Proy. J. Math., 26, pp. 253-257, (2007).        [ Links ]

[Sch] H. Schaefer, Topological Vector Spaces, MacMillan, N. Y., (1966).        [ Links ]

[Sw] C. Swartz, An Introduction to Functional Analysis, Marcel Dekker, N. Y., (1992).        [ Links ]

[Tr] F. Treves, Topological Vector Spaces, Distributions and Kernels, Academic Press, N. Y., (1967).        [ Links ]

[Wi] A. Wilansky, Modern Methods in Topological Vector Spaces, McGraw-Hill, N. Y., (1978).        [ Links ]

Charles Swartz
Mathematics Department
New Mexico State University
Las Cruces, N. M., 88003
U. S. A.
e-mail : cswartz@nmsu.edu


Received : July 2009. Accepted : August 2009