Infiniteness of the Number of Eigenvalues Embedded in the Essential Spectrum of a \(2\times2\) Operator Matrix


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Authors

  • M.I. Muminov
  • T.H. Rasulov

Keywords:

block operator matrix, bosonic Fock space, discrete and essential spectra, eigenvalues embedded in the essential spectrum, discrete spectrum asymptotics, Birman-Schwinger principle, Hilbert-Schmidt class

Abstract

In the present paper a \(2\times2\) block operator matrix H is considered as a bounded self-adjoint operator in the direct sum of two Hilbert spaces. The structure of the essential spectrum of 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 H.

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Published

2014-06-30

How to Cite

Muminov, M., & Rasulov, T. (2014). Infiniteness of the Number of Eigenvalues Embedded in the Essential Spectrum of a \(2\times2\) Operator Matrix. Eurasian Mathematical Journal, 5(2), 60–77. Retrieved from https://emj.enu.kz/index.php/main/article/view/571

Issue

Vol. 5 No. 2 (2014)

Section

Articles