On the number of components of the essential spectrum of one $2\times2$ operator matrix

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).