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thehardyreader
  • Member for 5 years, 5 months
  • Last seen more than 3 years ago
  • Wien, Österreich
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"Irrtum verläßt uns nie, doch ziehet ein hoher Bedürfnis Immer den strebenden Geist leise zur Wahrheit hinan." - Johann Wolfgang von Goethe

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12
Calculate the operator norm of $A: L^2[0,1] \to L^2[0,1]$ defined by $(Af)(x):=i\int_0^x f(t)\,dt-\frac{i}{2} \int_0^1 f(t) \,dt$
7
Prove that $\sum\limits_{i\leq n} a_n X_n$ converges almost surely iff $\sum\limits_{i\leq n}a_n^2$ converges.