### Abstract

V. Sunder proved that for n×n complex matrices A and B, with A being Hermitian and B being skew Hermitian with eigenvalues {αi}ni=1{αi}i=1n and {βi}ni=1{βi}i=1n respectively (counting multiplicity) such that

|α1|≥⋯≥|αn|,|β1|≤⋯≤|βn|

|α1|≥⋯≥|αn|,|β1|≤⋯≤|βn|

then

|αi−βi|≤∥A−B∥

|αi−βi|≤∥A−B∥

where ∥⋅∥∥⋅∥ is the operator bound norm. We generalize Sunder’s result to the case of an m-tuple of n × n complex matrices, using the Clifford operator.

|α1|≥⋯≥|αn|,|β1|≤⋯≤|βn|

|α1|≥⋯≥|αn|,|β1|≤⋯≤|βn|

then

|αi−βi|≤∥A−B∥

|αi−βi|≤∥A−B∥

where ∥⋅∥∥⋅∥ is the operator bound norm. We generalize Sunder’s result to the case of an m-tuple of n × n complex matrices, using the Clifford operator.

Original language | English |
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Title of host publication | Operator Algebras and Mathematical Physics: 24th International Workshop in Operator Theory and its Applications, Bangalore, December 2013 (IWOTA 2013) |

Editors | Tirthankar Bhattacharyya, Michael A Dritschel |

Place of Publication | Cham Switzerland |

Publisher | Springer |

Pages | 83-86 |

Number of pages | 4 |

Volume | 247 |

ISBN (Electronic) | 9783319181820 |

ISBN (Print) | 9783319181813 |

DOIs | |

Publication status | Published - 2015 |

Event | International Workshop on Operator Theory and its Applications (IWOTA) 2013 - Indian Institute of Science, Bangalore, India Duration: 16 Dec 2013 → 20 Dec 2013 Conference number: 24th http://math.iisc.ernet.in/~iwota2013/ |

### Workshop

Workshop | International Workshop on Operator Theory and its Applications (IWOTA) 2013 |
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Abbreviated title | IWOTA 2013 |

Country | India |

City | Bangalore |

Period | 16/12/13 → 20/12/13 |

Internet address |

### Keywords

- Joint eigenvalues
- joint spectra
- Clifford algebra
- commuting tuple of matrices
- Sunder’s inequality

### Cite this

Jhanjee, S., & Pryde, A. J. (2015). Generalized Sunder inequality. In T. Bhattacharyya, & M. A. Dritschel (Eds.),

*Operator Algebras and Mathematical Physics: 24th International Workshop in Operator Theory and its Applications, Bangalore, December 2013 (IWOTA 2013)*(Vol. 247, pp. 83-86). Cham Switzerland: Springer. https://doi.org/10.1007/978-3-319-18182-0_5