Spectral enclosures for a class of block operator matrices

Juan Giribet; Matthias Langer; Francisco Martínez Pería; Friedrich Philipp; Carsten Trunk

doi:10.1016/j.jfa.2019.108455

Spectral enclosures for a class of block operator matrices

Juan Giribet, Matthias Langer, Francisco Martínez Pería, Friedrich Philipp, Carsten Trunk

Mathematics And Statistics

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Abstract

We prove new spectral enclosures for the non-real spectrum of a class of 2×2 block operator matrices with self-adjoint operators A and D on the diagonal and operators B and -B* as off-diagonal entries. One of our main results resembles Gershgorin's circle theorem. The enclosures are applied to J-frame operators.

Original language	English
Article number	108455
Number of pages	24
Journal	Journal of Functional Analysis
Volume	278
Issue number	10
Early online date	2 Jan 2020
DOIs	https://doi.org/10.1016/j.jfa.2019.108455
Publication status	Published - 1 Jun 2020

Keywords

block operator matrix
quadratic numerical range
spectral enclosure
Gershgorin's circle

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10.1016/j.jfa.2019.108455

Giribet-etal-JFA-2020-Spectral-enclosures-for-a-class-of-block-operator-matricesAccepted author manuscript, 692 KBLicence: CC BY-NC-ND 4.0

Cite this

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title = "Spectral enclosures for a class of block operator matrices",

abstract = "We prove new spectral enclosures for the non-real spectrum of a class of 2×2 block operator matrices with self-adjoint operators A and D on the diagonal and operators B and -B* as off-diagonal entries. One of our main results resembles Gershgorin's circle theorem. The enclosures are applied to J-frame operators.",

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AU - Giribet, Juan

AU - Langer, Matthias

AU - Martínez Pería, Francisco

AU - Philipp, Friedrich

AU - Trunk, Carsten

PY - 2020/6/1

Y1 - 2020/6/1

N2 - We prove new spectral enclosures for the non-real spectrum of a class of 2×2 block operator matrices with self-adjoint operators A and D on the diagonal and operators B and -B* as off-diagonal entries. One of our main results resembles Gershgorin's circle theorem. The enclosures are applied to J-frame operators.

AB - We prove new spectral enclosures for the non-real spectrum of a class of 2×2 block operator matrices with self-adjoint operators A and D on the diagonal and operators B and -B* as off-diagonal entries. One of our main results resembles Gershgorin's circle theorem. The enclosures are applied to J-frame operators.

KW - block operator matrix

KW - quadratic numerical range

KW - spectral enclosure

KW - Gershgorin's circle

UR - https://www.sciencedirect.com/journal/journal-of-functional-analysis

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DO - 10.1016/j.jfa.2019.108455

M3 - Article

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VL - 278

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 10

M1 - 108455

ER -

Spectral enclosures for a class of block operator matrices

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Matthias Langer

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Spectral enclosures for a class of block operator matrices

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Matthias Langer

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