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Possible Duplicate:
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.

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marked as duplicate by Andreas Thom, Bill Johnson, Matthew Daws, Yemon Choi, Alain Valette Jan 8 '12 at 6:30

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

This appears to be identical to which was closed two days ago. It seems pointless to just repeat a question which the community felt was not suitable for this site... – Matthew Daws Jan 7 '12 at 17:35

In you can find a weighted shift operator that has this property.

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