A Banach space with a non-complemented closed subspace.

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c_{∘} is a non-complemented closed subspace of l^{∞}. (cf. [R.S. Philips, On linear transformations, Trans Amer Math. Soc. 48 (1940), 516-554.])

Newmann and Rudin gave another example, i.e. the subspace of C(T) consisting of the boundary values of analytic functions. (cf. [K. Hofman, Banach spaces of analytic functions, Prentice-Hall, Englewood Cliffs, N.J. 1962.])