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norms.doc
Prove rigorously that ||x + y||1 <= ||x||1 + ||y||1
Bounded Linear Operator : Bounded Invertible an Norm - 11.8 Let and where a "1" appears in the n-th position and a zero in all other positions. Let (an) be a sequence of complex numbers. Prove then that
(i) ... defines a bounded linear operato ...
Subspace of Inner Product Space and Finite Dimensional Space - 1. (i) Let W C V be a subspace of an inner product space V . Prove that W C (W) .
(ii) If, in addition, V is finite dimensional, prove that W = (W).
Please see the attached file for the fully ...
Sup norm question - Let X be a compact metric space and Y be a normed space.
Prove that if f_n belongs to C(X,Y), then lim_n f_n = f_o in the Sup norm
if and only if lim_n f_n = f_o uniformly in X.
[ Note: Sup nor ...