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I have difficulty proving:

If $T$ is a normal operator in a Hilbert space, $T$ is surjective if and only if $T^*$ surjective.

Please give me some help. Thank you.

  • 1
    Is $T$ assumed to be bounded? If so, $T$ is actually invertible, hence so is $T^*$.2012-12-29
  • 0
    @JonasMeyer: Nice observation!2012-12-29

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