Sectoriality and Essential Spectrum of Non Symmetric Graph Laplacians

We consider a non self-adjoint Laplacian on a directed graph with non symmetric edge weights. We give sufficient conditions for this Laplacian to be sectorial. We introduce a special self-adjoint operator and compare its essential spectrum with that of the non self-adjoint Laplacian considered.

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Bibliographic Details
Published in:	Complex analysis and operator theory Vol. 13; no. 3; pp. 967 - 983
Main Authors:	Anné, Colette, Balti, Marwa, Torki-Hamza, Nabila
Format:	Journal Article
Language:	English
Published:	Cham Springer International Publishing 01-04-2019 Springer Nature B.V Springer Verlag
Subjects:	Analysis Graph theory Mathematics Mathematics and Statistics Operator Theory Spectral Theory Non self-adjoint Laplacian Numerical range 47B25 Essential spectrum 39A12 47B37 Sectorial operator 47A45 47A12 47A10 Directed graph
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Description
Summary:	We consider a non self-adjoint Laplacian on a directed graph with non symmetric edge weights. We give sufficient conditions for this Laplacian to be sectorial. We introduce a special self-adjoint operator and compare its essential spectrum with that of the non self-adjoint Laplacian considered.
ISSN:	1661-8254 1661-8262
DOI:	10.1007/s11785-018-0817-2