JournalsjstVol. 2, No. 4pp. 355–371

Polynomials of almost normal arguments in CC^*-algebras

  • Nikolai D. Filonov

    Steklov Mathematical Institute, St. Petersburg, Russian Federation
  • Ilya Kachkovskiy

    King's College, London, UK
Polynomials of almost normal arguments in  $C^*$-algebras cover
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Abstract

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

Cite this article

Nikolai D. Filonov, Ilya Kachkovskiy, Polynomials of almost normal arguments in CC^*-algebras. J. Spectr. Theory 2 (2012), no. 4, pp. 355–371

DOI 10.4171/JST/33