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Hilbert Space and Subspace

Problem. Show that if is an orthonormal set in a Hilbert space H, then the set of all vectors of the form is a subspace of H.

Hint: Take a Cauchy sequence , where . Set and show that is a Cauchy sequence in .

Please see the attached file for full problem description.

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Solution Summary

A Hilbert Space and Subspace are investigated. The solution is detailed and well presented.

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