Compact operators

Authors

  • Charles Swartz New Mexico State University.

DOI:

https://doi.org/10.4067/S0716-09172009000300004

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.

Author Biography

Charles Swartz, New Mexico State University.

Mathematics Department.

References

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

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

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

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

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

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

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

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

How to Cite

[1]
C. Swartz, “Compact operators”, Proyecciones (Antofagasta, On line), vol. 28, no. 3, pp. 233-237, 1.

Issue

Section

Artículos