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## Main Question or Discussion Point

a linear operator T: X -> Y is bounded if there exists M>0 such that:

ll Tv ll

conversely, if i know this inequality is true, is it always true that T: X ->Y and is linear?

ll Tv ll

_{Y}[tex]\leq[/tex] M*ll v ll_{X}for all v in Xconversely, if i know this inequality is true, is it always true that T: X ->Y and is linear?

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