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A Note on J-positive Block Operator Matrices

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Abstract

We study basic spectral properties of \({\mathcal{J}}\)-self-adjoint 2 × 2 block operator matrices. Using the linear resolvent growth condition, we obtain simple necessary conditions for the regularity of the critical point ∞. We apply our results to the linearized operator arising in the study of soliton type solutions to the nonlinear relativistic Ginzburg–Landau equation.

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Authors and Affiliations

  1. Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, 1090, Vienna, Austria

    Aleksey Kostenko

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  1. Aleksey Kostenko
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Correspondence to Aleksey Kostenko.

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Research supported by the Austrian Science Fund (FWF) under Grant No. P26060.

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Kostenko, A. A Note on J-positive Block Operator Matrices. Integr. Equ. Oper. Theory 81, 113–125 (2015). https://doi.org/10.1007/s00020-014-2156-7

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  • DOI: https://doi.org/10.1007/s00020-014-2156-7

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