Geodesic
Infiniteness of the number of eigenvalues embedded in the essential spectrum of a~$2\times2$ operator matrix
Eurasian mathematical journal, Tome 5 (2014) no. 2, pp. 60-77

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In the present paper a $2\times2$ block operator matrix $\mathbf H$ is considered as a bounded self-adjoint operator in the direct sum of two Hilbert spaces. The structure of the essential spectrum of $\mathbf H$ is studied. Under some natural conditions the infiniteness of the number of eigenvalues is proved, located inside, in the gap or below the bottom of the essential spectrum of $\mathbf H$. 
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     title = {Infiniteness of the number of eigenvalues embedded in the essential spectrum of a~$2\times2$ operator matrix},
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M. I. Muminov; T. H. Rasulov. Infiniteness of the number of eigenvalues embedded in the essential spectrum of a~$2\times2$ operator matrix. Eurasian mathematical journal, Tome 5 (2014) no. 2, pp. 60-77. http://geodesic.mathdoc.fr/item/EMJ_2014_5_2_a3/