A note on J-positive block operator matrices

Abstract

We study basic spectral properties of J-self-adjoint $2\times 2$ block operator matrices. Using the linear resolvent growth condition, we obtain simple necessary conditions for the regularity of the critical point $\infty$. In particular, we present simple examples of operators having the singular critical point $\infty$. Also, we apply our results to the linearized operator arising in the study of soliton type solutions to the nonlinear relativistic Ginzburg-Landau equation.

11 pages

References in corpus (2)

• Asymptotic stability of Landau solutions to Navier-Stokes system
• On eigenfunction expansion of solutions to the Hamilton equations