Distance to normal elements in $C^{\ast }$-algebras of real rank zero

Abstract

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 $\Vert [A,A^{\ast }]\Vert$ and the distance to the set of invertible operators. A slightly modified estimate holds in a general $C^{\ast }$-algebra of real rank zero.

22 pages, 10 figures. The introduction has been rewritten as the referees suggested. Some other minor amendments in the text were made, J. Amer. Math. Soc. electronically published on January 8, 2015

References in corpus (1)

• On the relation between an operator and its self-commutator

Cited by in corpus (2)

• Randomized Joint Diagonalization of Symmetric Matrices
• Certification of two-qubit quantum systems with temporal inequality