Closed Graph Theorem
المؤلف:
Conway, J. B.
المصدر:
A Course in Functional Analysis. New York: Springer-Verlag, 1990.
الجزء والصفحة:
...
5-7-2021
1658
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" ![<span style=]()
{(x,f(x)):x in X}" src="https://mathworld.wolfram.com/images/equations/ClosedGraphTheorem/Inline3.gif" style="height:15px; width:103px" /> 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.
الاكثر قراءة في التبلوجيا
اخر الاخبار
اخبار العتبة العباسية المقدسة
