Question

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Quasinilpotent operator

Do you know any example of a quasinilpotent operator such that every its power is non-compact?

Of course direct sum of nilpotent operators(or Volterra operator) can by good. But I search for same known("classical") example.

Answer 1

In http://www.jstor.org/pss/2047905 you can find a weighted shift operator that has this property.