Multiparameter System of Operators with Two Parameters in Finite Dimensional Spaces
Pure and Applied Mathematics Journal
Volume 4, Issue 4-1, August 2015, Pages: 1-4
Received: Feb. 25, 2015; Accepted: Feb. 27, 2015; Published: May 12, 2015
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Authors
Rakhshanda Dzhabarzadeh, Department of functional analysis, Institute of Mathematics and Mechanics of NAS of Azerbaijan, Baku
Afet Jabrailova, Department of functional analysis, Institute of Mathematics and Mechanics of NAS of Azerbaijan, Baku
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Abstract
The authors have proved the existence of the multiple basis on the eigen and associated elements of the two parameter system of operators in finite dimensional spaces. The proof uses the notion of the abstract analog of resultant of two operator pencils, acting, generally speaking, in different Hilbert spaces. In this paper necessary and sufficient conditions of the existence of multiple completeness of the eigen and associated vectors of two parameter system of operators in finite dimensional Hilbert space is given.
Keywords
Multiparameter, Spectrum, Operator, Space, Eigenvector
To cite this article
Rakhshanda Dzhabarzadeh, Afet Jabrailova, Multiparameter System of Operators with Two Parameters in Finite Dimensional Spaces, Pure and Applied Mathematics Journal. Special Issue: Spectral Theory of Multiparameter Operator Pencils and Its Applications. Vol. 4, No. 4-1, 2015, pp. 1-4. doi: 10.11648/j.pamj.s.2015040401.11
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