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

Ilya Kachkovskiy; Yuri Safarov

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

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

Operator Algebras 2015-02-24 v3 Functional Analysis Spectral Theory

Authors: Ilya Kachkovskiy , Yuri Safarov

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

Keywords

$C^*$-algebra real rank zero normal operator bounded operator distance estimate invertible operator

Cite

@article{arxiv.1403.2021,
  title  = {Distance to normal elements in $C^*$-algebras of real rank zero},
  author = {Ilya Kachkovskiy and Yuri Safarov},
  journal= {arXiv preprint arXiv:1403.2021},
  year   = {2015}
}

Comments

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

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

Abstract

Keywords

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