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Thread: boundedness and linear operators question

  1. #1
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    boundedness and linear operators question

    Hi i'm having trouble with this:

    Consider a linear operator from a Banach space X to X. Let X=L2(0,1) (lebesgue space with p=2). Give an example of a (densely defined) linear operator A which is unbounded from X to X?
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  2. #2
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    You could take the operator to be the operation of differentiation. Of course, you'll have to explain why it is (a) densely defined and (b) unbounded.
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