On the Number of Components of the Essential Spectrum of One 2 × 2 Operator Matrix
M. I. MuminovSamarkand State University, 140104, Samarkand, Republic of UzbekistanI. N. BozorovRomanovsky Institute of Mathematics, Academy of Sciences of Uzbekistan, 100174, Tashkent, Republic of UzbekistanTulkin H. RasulovBukhara State University, 200118, Bukhara, Republic of Uzbekistan
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Аннотация
In this paper, a $$2 \times 2$$ block operator matrix $$H$$ is considered as a bounded and self-adjoint operator in a Hilbert space. The location of the essential spectrum $${{\sigma }_{{{\text{ess}}}}}(H)$$ 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 $${{\sigma }_{{{\text{ess}}}}}(H)$$ are singled out. We prove that the essential spectrum $${{\sigma }_{{{\text{ess}}}}}(H)$$ consists of no more than six segments (components).
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