4
$\begingroup$

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

$\endgroup$
2
  • $\begingroup$ Do you mean the (norm-)closed algebra generated by $A$ and $A*$? $\endgroup$
    – Yemon Choi
    Oct 15, 2011 at 1:50
  • $\begingroup$ @Yemon Choi : no, not the norm-closed algebra. I mean the non-commutative polynomials in A and $A^{*}$ . $\endgroup$
    – jjcale
    Oct 15, 2011 at 12:17

0

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Browse other questions tagged or ask your own question.