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

Improve this question
$\endgroup$
2
  • $\begingroup$ Do you mean the (norm-)closed algebra generated by $A$ and $A*$? $\endgroup$
    – Yemon Choi
    Commented 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
    Commented Oct 15, 2011 at 12:17

0

Reset to default

You must log in to answer this question.

Browse other questions tagged .