On the Number of Components of the Essential Spectrum of One 2 × 2 Operator Matrix

Annotatsiya

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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Identifikatorlar

DOI

10.3103/s1066369x24700129

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