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Functional analysis convergence question

  1. Apr 8, 2010 #1
    If [tex]X[/tex] is Banach space and [tex]F:X \rightarrow X[/tex] is a linear and bounded map and that [tex]F^n(x)\rightarrow0[/tex] pointwise .. How can I show that it converges to zero uniformly also?

    Last edited: Apr 8, 2010
  2. jcsd
  3. Apr 9, 2010 #2
    http: //en.wikipedia.org/wiki/Bounded_operator#Equivalence_of_boundedness_and_continuity
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