Compact operators
DOI:
https://doi.org/10.4067/S0716-09172009000300004Abstract
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
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[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).
[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.
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