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We show next that the mapping T can be extended uniquely to an isomorphism
fromHX ontoK . if Y 2HX then there is a sequence Yn 2HX such that kYn−Yk! 0. This implies that Yn is a Cauchy sequence and hence, since T is norm-preserving,
the sequence {TYn} is Cauchy in L2(F). The sequence {TYn} therefore converges
in norm to an element of K .
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