## Constructive Functional Analysis |

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Alg(r algebra belong best approximation Cauchy sequence Chapter choose in turn classical compact metric space compact subset compact support complemented set complete computable constructive mathematics constructive proof continuous mapping converges in measure convex countably define dmn f e-net element equivalent essentially non-constructive f in C(X follows full set functional calculus G C(X G Z+ Given Hence Hilbert space Hom(E,F homeomorphic hyperinjective integrable function integrable set Let f linear subspace llfll llull llxll locally compact space located subset Math metric space Moreover n e Z+ nonvoid normed space O-connected orthonormal basis pointwise positive integer positive numbers precompact proper compact interval Prove real numbers resp selfadjoint Stone-Weierstrass Theorem strong operator norm subfinite suppose Theorem thick norm uniform uniformly continuous uniformly continuous mapping weak operator norm whence