Polynomials of almost-normal arguments in $C^{\ast }$-algebras

Abstract

The functional calculus for normal elements in $C^{\ast }$-algebras is an important tool of analysis. We consider polynomials $p(a,a^{\ast })$ for elements $a$ with small self-commutator norm $\Vert [a,a^{\ast }]\Vert \le \delta$ and show that many properties of the functional calculus are retained modulo an error of order $\delta$.

The paper has been restructured. Accepted for publication in Journal of Spectral Theory, European Mathematical Society