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Title: Quaternionic triangular linear operators
Author: Cerejeiras, Paula
Colombo, Fabrizio
Käehler, Uwe
Sabadini, Irene
Keywords: Triangular quaternionic operators
S-resolvent operators
Slice hyperholomorphic functions
Issue Date: 30-Jan-2023
Publisher: Wiley
Abstract: Triangular operators are an essential tool in the study of non-selfadjoint operators that appear in different fields with a wide range of applications. Although the development of a quaternionic counterpart for this theory started at the beginning of this century, the lack of a proper spectral theory combined with problems caused by the underlying noncommutative structure prevented its real development for a long time. In this paper, we give criteria for a quaternionic linear operator to have a triangular representation, namely, under which conditions such operators can be represented as a sum of a diagonal operator with a Volterra operator. To this effect, we investigate quaternionic Volterra operators based on the quaternionic spectral theory arising from the S-spectrum.This allow us to obtain conditions when a non-selfadjoint operator admits a triangular representation.
Peer review: yes
DOI: 10.1002/mma.8631
ISSN: 0170-4214
Publisher Version:
Appears in Collections:CIDMA - Artigos
DMat - Artigos
CHAG - Artigos

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