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A ``pointwise-bounded'' family of continuous linear Operators from a Banach Space to a
Normed Space is ``uniformly bounded.'' Symbolically, if
is Finite for each
in the
unit Ball, then
is Finite. The theorem is also called the Banach-Steinhaus Theorem.
References
Zeidler, E. Applied Functional Analysis: Applications to Mathematical Physics.
New York: Springer-Verlag, 1995.