### Abstract

The meta theorem of this paper is that Halmos’ two projections theorem is something like Robert Sheckley’s Answerer: no question about the W^{*}- and C^{*}-algebras generated by two orthogonal projections will go unanswered, provided the question is not foolish. An alternative approach to questions about two orthogonal projections makes use of the supersymmetry equality introduced by Avron, Seiler, and Simon. A noteworthy insight of the paper reveals that the supersymmetric approach is nothing but Halmos in different language and hence an equivalent Answerer.

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 | 125-138 |

Number of pages | 14 |

DOIs | |

State | Published - Jan 1 2018 |

### Publication series

Name | Operator Theory: Advances and Applications |
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Volume | 268 |

ISSN (Print) | 0255-0156 |

ISSN (Electronic) | 2296-4878 |

### Keywords

- C-algebra
- Drazin inverse
- Fredholm operator
- Orthogonal projection
- Trace-class operator
- W-algebra

### ASJC Scopus subject areas

- Analysis

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## Cite this

Böttcher, A., & Spitkovsky, I. M. (2018). Robert Sheckley’s Answerer for two orthogonal projections. In

*Operator Theory: Advances and Applications*(pp. 125-138). (Operator Theory: Advances and Applications; Vol. 268). Springer International Publishing. https://doi.org/10.1007/978-3-319-75996-8_6