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Date: 13-5-2021
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The closed graph theorem states that a linear operator between two Banach spaces and is continuous iff it has a closed graph, where the "graph" is considered closed if it is a closed subset of equipped with the product topology.
The closed graph theorem also holds for Fréchet spaces.
REFERENCES:
Conway, J. B. A Course in Functional Analysis. New York: Springer-Verlag, 1990.
Zeidler, E. Applied Functional Analysis: Applications to Mathematical Physics. New York: Springer-Verlag, 1995.
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