Email this article Investigations of the numerical range of a operator matrix
- Authors: Rasulov T.K.1, Dilmurodov E.B1
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Affiliations:
- Bukhara State University
- Issue: Vol 18, No 2 (2014)
- Pages: 50-63
- Section: Articles
- URL: https://bakhtiniada.ru/1991-8615/article/view/20726
- DOI: https://doi.org/10.14498/vsgtu1275
- ID: 20726
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Abstract
We consider a $2\times2$ operator matrix $A$ (so-called generalized Friedrichs model) associated with a system of at most two quantum particles on ${\rm d}$-dimensional lattice. This operator matrix acts in the direct sum of zero- and one-particle subspaces of a Fock space. We investigate the structure of the closure of the numerical range $W(A)$ of this operator in detail by terms of its matrix entries for all dimensions of the torus ${\bf T}^{\rm d}$. Moreover, we study the cases when the set $W(A)$ is closed and give necessary and sufficient conditions under which the spectrum of $A$ coincides with its numerical range.
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##article.viewOnOriginalSite##About the authors
Tulkin Kh Rasulov
Bukhara State University
Email: rth@mail.ru
(Cand. Phys. & Math. Sci.), Assotiate Professor, Dept. of Mathematical Physics & Analysis 11, Muhammad Igbol st, Bukhara, 200100, Uzbekistan
Elyor B Dilmurodov
Bukhara State University
Email: elyor.dilmurodov@mail.ru
Assistant Lecturer, Dept. of Mathematical Physics & Analysis 11, Muhammad Igbol st, Bukhara, 200100, Uzbekistan
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