Distance to normal elements in 𝐶*-algebras of real rank zero

Kachkovskiy, Ilya¹ ; Safarov, Yuri²

¹Department of Mathematics, University of California, Irvine, Irvine, California 92697-3875
²Department of Mathematics, King’s College London, Strand, London WC2R 2LS, United Kingdom

Journal of the American Mathematical Society, Tome 29 (2016) no. 1, pp. 61-80

Résumé

We obtain an order sharp estimate for the distance from a given bounded operator $A$ on a Hilbert space to the set of normal operators in terms of $\|[A,A^*]\|$ and the distance to the set of invertible operators. A slightly modified estimate holds in a general $C^*$-algebra of real rank zero.

Détail

DOI : 10.1090/S0894-0347-2015-00823-2

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