### Abstract

The criterion is obtained for operators A from the algebra generated by two orthogonal projections P, Q to have a compatible range, i.e., coincide with A* on the orthogonal complement to the sum of the kernels of A and A*. In the particular case of A being a polynomial in P, Q, some easily verifiable conditions are derived.

Original language | English (US) |
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Pages (from-to) | 117-122 |

Number of pages | 6 |

Journal | Advances in Operator Theory |

Volume | 3 |

Issue number | 1 |

DOIs | |

State | Published - Dec 1 2018 |

### Fingerprint

### Keywords

- Hermitian operators
- Orthogonal projections
- Von Neumann algebras

### ASJC Scopus subject areas

- Algebra and Number Theory
- Analysis

### Cite this

**Operators with compatible ranges in an algebra generated by two orthogonal projections.** / Spitkovsky, Ilya.

Research output: Contribution to journal › Article

*Advances in Operator Theory*, vol. 3, no. 1, pp. 117-122. https://doi.org/10.22034/aot.1702-1111

}

TY - JOUR

T1 - Operators with compatible ranges in an algebra generated by two orthogonal projections

AU - Spitkovsky, Ilya

PY - 2018/12/1

Y1 - 2018/12/1

N2 - The criterion is obtained for operators A from the algebra generated by two orthogonal projections P, Q to have a compatible range, i.e., coincide with A* on the orthogonal complement to the sum of the kernels of A and A*. In the particular case of A being a polynomial in P, Q, some easily verifiable conditions are derived.

AB - The criterion is obtained for operators A from the algebra generated by two orthogonal projections P, Q to have a compatible range, i.e., coincide with A* on the orthogonal complement to the sum of the kernels of A and A*. In the particular case of A being a polynomial in P, Q, some easily verifiable conditions are derived.

KW - Hermitian operators

KW - Orthogonal projections

KW - Von Neumann algebras

UR - http://www.scopus.com/inward/record.url?scp=85046280359&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85046280359&partnerID=8YFLogxK

U2 - 10.22034/aot.1702-1111

DO - 10.22034/aot.1702-1111

M3 - Article

AN - SCOPUS:85046280359

VL - 3

SP - 117

EP - 122

JO - Advances in Operator Theory

JF - Advances in Operator Theory

SN - 2538-225X

IS - 1

ER -