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Quaternionic triangular linear operators.
- Source :
-
Mathematical Methods in the Applied Sciences . 1/30/2023, Vol. 46 Issue 2, p2093-2116. 24p. - Publication Year :
- 2023
-
Abstract
- Triangular operators are an essential tool in the study of nonselfadjoint 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. [ABSTRACT FROM AUTHOR]
- Subjects :
- *VOLTERRA operators
*SPECTRAL theory
Subjects
Details
- Language :
- English
- ISSN :
- 01704214
- Volume :
- 46
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- Mathematical Methods in the Applied Sciences
- Publication Type :
- Academic Journal
- Accession number :
- 160872399
- Full Text :
- https://doi.org/10.1002/mma.8631