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

Ilya Kachkovskiy; Yuri Safarov

arxiv: 1403.2021 · v3 · pith:ZRGA7ZYVnew · submitted 2014-03-09 · 🧮 math.OA · math.FA· math.SP

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

Ilya Kachkovskiy , Yuri Safarov This is my paper

classification 🧮 math.OA math.FAmath.SP

keywords distanceestimatenormaloperatorsrankrealzeroalgebra

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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.

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

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