. Let X be a Banach space over the complex field C, and suppose M is a closed subspace of X. Prove that if T:M + ((N) is

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Let X Be A Banach Space Over The Complex Field C And Suppose M Is A Closed Subspace Of X Prove That If T M N Is 1 (23.96 KiB) Viewed 22 times

. Let X be a Banach space over the complex field C, and suppose M is a closed subspace of X. Prove that if T:M + ((N) is a bounded linear operator, then there is a bounded linear extension S: X + (%(N) such that ||$|| = ||T||. (Recall that S is a linear extension of T from M to X if S(m) = T(m) for all m in M.) a =