1.Show that an operator T on a Hilbert Space H is unitary iff
T(šš) complete orthonormal set whenever šš
is.
Hilbert space H1 has some orthonormal basis {ei}iāI . Then since unitary operator T maps any orthonormal basis of H1to an orthonormal basis of H2, then specifically {T(ei)}iāI must be an orthonormal basis of H2.
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