Suppose Y is a closed subspace of a normedlinear space X and xo E Y, x, e X . Provethat there is a linear functional fo e X1 suchthat fo(xo) = d(xg, y), fo(Y) =0 and |\foll =1.

Y is a closed subspace of a normed linear space X and x0∉Y, x0∈X.. We have to prove that there is a…

Answered: Suppose Y is a closed subspace of a…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Suppose Y is a closed subspace of a normed linear space X and xo ¤ Y, x, € X . Prove that there is a linear functional fo e X1 such that fo(xo) =d(x y), fo(Y) =0 and ||foll =1.