### Abstract

Let u be a Hermitian involution, and e an orthogonal projection, acting on the same Hilbert space H. We establish the exact formula, in terms of ║eue║, for the distance from e to the set of all orthogonal projections q from the algebra generated by e, u, and such that quq = 0.

Original language | English (US) |
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Title of host publication | Operator Theory |

Subtitle of host publication | Advances and Applications |

Publisher | Springer International Publishing |

Pages | 371-376 |

Number of pages | 6 |

DOIs | |

State | Published - Jan 1 2018 |

### Publication series

Name | Operator Theory: Advances and Applications |
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Volume | 267 |

ISSN (Print) | 0255-0156 |

ISSN (Electronic) | 2296-4878 |

### Keywords

- C-algebra
- Involution
- Orthogonal projection
- W-algebra

### ASJC Scopus subject areas

- Analysis

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## Cite this

Spitkovsky, I. M. (2018). A Distance Formula Related to a Family of Projections Orthogonal to Their Symmetries. In

*Operator Theory: Advances and Applications*(pp. 371-376). (Operator Theory: Advances and Applications; Vol. 267). Springer International Publishing. https://doi.org/10.1007/978-3-319-72449-2_17