Sign up ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

Let A be a quasinilpotent operator on a Hilbert space and let every operator of the algebra generated by $A$ and $A^{*}$ have finite spectrum. Does then follow, that A is nilpotent ?

See also quasinilpotence and finite spectrum and Finite-dimensional subalgebras of $C^\star$-algebras

share|cite|improve this question
Do you mean the (norm-)closed algebra generated by $A$ and $A*$? – Yemon Choi Oct 15 '11 at 1:50
@Yemon Choi : no, not the norm-closed algebra. I mean the non-commutative polynomials in A and $A^{*}$ . – jjcale Oct 15 '11 at 12:17

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.