Rasulov, Tulkin; Tretter, Christiane
(2018).
*
Spectral inclusion for unbounded diagonally dominant n × n operator matrices.
*
Rocky Mountain journal of mathematics, 48(1), pp. 279-324.
Rocky Mountain Mathematics Consortium
10.1216/RMJ-2018-48-1-279

In this paper, we establish an analytic enclosure for the spectrum of unbounded linear operators ~A admitting an n×n matrix representation in a Hilbert space H=H₁⊕⋯⊕Hn. For diagonally dominant operator matrices of order 0, we show that this new enclosing set, the block numerical range Wⁿ(A), contains the eigenvalues of A and that the approximate point spectrum of A is contained in its closure Wⁿ(A). Since the block numerical range turns out to be a subset of the usual numerical range, Wⁿ(A)⊂W(A), it may give a tighter enclosure of the spectrum. Moreover, we prove Gershgorin theorems for diagonally dominant n×n operator matrices and compare our results to both Gershgorin bounds and classical perturbation theory. Our results are illustrated by deriving new lower bounds for 3×3 self-adjoint operator matrices and applying the latter to three-channel Hamiltonians in quantum~mechanics.

## Item Type: |
Journal Article (Original Article) |
---|---|

## Division/Institute: |
08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematics |

## UniBE Contributor: |
Rasulov, Tulkin and Tretter, Christiane |

## Subjects: |
500 Science > 510 Mathematics |

## ISSN: |
0035-7596 |

## Publisher: |
Rocky Mountain Mathematics Consortium |

## Language: |
English |

## Submitter: |
Olivier Bernard Mila |

## Date Deposited: |
22 May 2019 14:31 |

## Last Modified: |
22 May 2019 14:31 |

## Publisher DOI: |
10.1216/RMJ-2018-48-1-279 |

## URI: |
https://boris.unibe.ch/id/eprint/125531 |