6-4 - Let X and Y be normed spaces and Z be a closed subspace of X. (a) Let F E BL(X,Y) and Z C Z(F). The map F: X/Z → Y given by F(r + Z) = F(r), z € X, is well-defined, F E BL(X/Z,Y) and |F|=|FI. (b) If F E BL(X/Z,Y) and we let F(x) = F(x + Z) for x € X, then FE BL(X,Y) and ||F|| = ||F||. 6-5 Let X be a normed space and f be a nonzero linear functional on X. Then f is discontinuous if and only if Z(f) is dense in X. 6-6 Let Y

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Q: be

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