Geodesic
On the number of components of the essential spectrum of one $2\times2$ operator matrix
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 2 (2024), pp. 85-90 Cet article a éte moissonné depuis la source Math-Net.Ru

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In this paper, a $2\times2$ block operator matrix $H$ is considered as a bounded and self-adjoint operator in a Hilbert space. The location of the essential spectrum $\sigma_{\rm ess}(H)$ of operator matrix $H$ is described via the spectrum of the generalized Friedrichs model, i.e. the two- and three-particle branches of the essential spectrum $\sigma_{\rm ess}(H)$ are singled out. We prove that the essential spectrum $\sigma_{\rm ess}(H)$ consists of no more than six segments (components).
Keywords: block operator matrix, eigenvalue, discrete spectrum, essential spectrum, component. 
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M. I. Muminov; I. N. Bozorov; T. Kh. Rasulov. On the number of components of the essential spectrum of one $2\times2$ operator matrix. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 2 (2024), pp. 85-90. http://geodesic.mathdoc.fr/item/IVM_2024_2_a5/

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