Question #272578

1.Show that an operator T on a Hilbert Space H is unitary iff


T(š‘’š‘–) complete orthonormal set whenever š‘’š‘–


is.

1
Expert's answer
2021-11-30T15:16:25-0500

Hilbert space H1 has some orthonormal basis {ei}i∈I . Then since unitary operator T maps any orthonormal basis of H1to an orthonormal basis of H2, then specifically {T(ei)}i∈I must be an orthonormal basis of H2.



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