On the number of components of the essential spectrum of one 2х2 operator matrix

In this paper, a 2х2 block operator matrix H is considered as a bounded and self-adjointoperator in a Hilbert space. The location of the essential σ 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 σ ess (H) are singled out. We prove that the essential spectrum σ ess (H) consists of no more than six segments (components).

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