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/Territory | 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