Prove that a linear functional on x is bounded if and only if i... | Filo
Prove that a linear functional on x is bounded if and only if i... | Filo
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SOLVED: 10. (Zero operator) Let T: X>X be a bounded linear operator on complex inner product space X If (Tx,x) = 0 for all xeX show that T=0. Show that this does not hold in the case of a real inner product space. Hint Consider a rotation of the Euclidean plane
SOLVED: 10. (Zero operator) Let T: X>X be a bounded linear operator …
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Let X and Y be normed spaces. Show that a linear operator T: X ⟶Y is bounded if and only if T maps bounded sets in X into bounded sets in Y. | Numerade
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