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Ian Morris
Ian Morris
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Yemon Choi
Yemon Choi
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Why isn't the theorem of approximation not appicableapplicable in banach-spacesBanach spaces?

Let X be a hilbert-spaceHilbert space, A a convex, closed subset of X. Then there exists for every x in X exactly one best approximation in A, that is there exists a y in A such that || x-y || = d(x,A) = inf { || x-z || : z in A}.

Why isn't that theorem true for banach-spacesBanach spaces?

Why isn't the theorem of approximation not appicable in banach-spaces?

Let X be a hilbert-space, A a convex, closed subset of X. Then there exists for every x in X exactly one best approximation in A, that is there exists a y in A such that || x-y || = d(x,A) = inf { || x-z || : z in A}.

Why isn't that theorem true for banach-spaces?

Why isn't the theorem of approximation applicable in Banach spaces?

Let X be a Hilbert space, A a convex, closed subset of X. Then there exists for every x in X exactly one best approximation in A, that is there exists a y in A such that || x-y || = d(x,A) = inf { || x-z || : z in A}.

Why isn't that theorem true for Banach spaces?

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Linda Raabe
Linda Raabe
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Why isn't the theorem of approximation not appicable in banach-spaces?

Let X be a hilbert-space, A a convex, closed subset of X. Then there exists for every x in X exactly one best approximation in A, that is there exists a y in A such that || x-y || = d(x,A) = inf { || x-z || : z in A}.

Why isn't that theorem true for banach-spaces?