Journal of Spectral Theory

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Volume 2, Issue 4, 2012, pp. 355–371
DOI: 10.4171/JST/33

Published online: 2012-06-24

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

Nikolai D. Filonov[1] and Ilya Kachkovskiy[2]

(1) Steklov Mathematical Institute, St. Petersburg, Russian Federation
(2) King's College, London, UK

The functional calculus for normal elements in $C^*$-algebras is an important tool of analysis. We suggest an approximate substitute for such calculus for elements $a$ with the small self-commutator norm $\|[a,a^*]\|\le \delta$. We show that many properties of the functional calculus are conserved up to order $\delta$.

Keywords: $C^*$-algebras, functional calculus, self-commutator, polynomials, Positivstellensatz, pseudospectrum

Filonov Nikolai, Kachkovskiy Ilya: Polynomials of almost normal arguments in $C^*$-algebras. J. Spectr. Theory 2 (2012), 355-371. doi: 10.4171/JST/33