Polynomials of almost-normal arguments in $C^*$-algebras
  The functional calculus for normal elements in $C^*$-algebras is an important tool of analysis. We consider polynomials $p(a,a^*)$ for elements $a$ with small self-commutator norm $\|[a,a^*]\| \le \delta$ and show that many properties of the functional calculus are retained modulo an error of order $\delta$. 
Nikolay Filonov, Ilya Kachkovskiy
math.OA math.AG math.SP