On the eigenvalues of a 2ˣ2 block operator matrix
M. I. MuminovUniversiti Teknologi Malaysia (UTM), Faculty of Science, 81310 Skudai, Johor Bahru, MalaysiaTulkin H. RasulovBukhara State University, Faculty of Physics and Mathematics, 11 M. Ikbol Str., Bukhara, 200100, Uzbekistan
ABI
Abstract
A 2 2 block operator matrix H acting in the direct sum of one-and two-particle subspaces of a Fock space is considered. The existence of infinitely many negative eigenvalues of H22 (the second diagonal entry of H) is proved for the case where both of the associated Friedrichs models have a zero energy resonance. For the number N (z) of eigenvalues of H22 lying below z < 0, the following asymptotics is found