Closed Graph Theorem

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.

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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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Closed Graph Theorem

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Weisstein, Eric W., with contributions by Mohammad Sal Moslehian. "Closed Graph Theorem." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/ClosedGraphTheorem.html

Closed Graph Theorem

See also

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References

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