Polynomials of almost-normal arguments in $C^*$-algebras

Ilya Kachkovskiy; Nikolay Filonov

arxiv: 1107.6010 · v2 · pith:TE3N2AAKnew · submitted 2011-07-29 · 🧮 math.OA · math.AG· math.SP

Polynomials of almost-normal arguments in C^*-algebras

Nikolay Filonov , Ilya Kachkovskiy This is my paper

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keywords algebrascalculusdeltaelementsfunctionalpolynomialsalmost-normalanalysis

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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 $\delta$.

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Polynomials of almost-normal arguments in C^*-algebras

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