An eigenvalue multiplicity formula for the Schur complement of a \(3\times3\) block operator matrix

DOI10.1134/S0037446615040126zbMath1323.47010OpenAlexW2190102146MaRDI QIDQ748479

M. E. Muminov, Tulkin H. Rasulov

Publication date: 29 October 2015

Published in: Siberian Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0037446615040126

zbMATH Keywords

Schur complementblock operator matrixcreation and annihilation operatorstrace class operatoressential and discrete spectrabosonic Fock spaceWeyl's inequality

Mathematics Subject Classification ID

Functions whose values are linear operators (operator- and matrix-valued functions, etc., including analytic and meromorphic ones) (47A56) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10)

Cites Work

• Expression for the number of eigenvalues of a Friedrichs model
• The spectrum of unbounded operator matrices with non-diagonal domain
• Some special properties of the generalized Friedrichs model
• The Efimov effect. Discrete spectrum asymptotics
• Schur complements and state space realizations
• The Schur complement and its applications
• A model in the theory of perturbations of the essential spectrum of multiparticle operators
• Spectral properties of the generalized Friedrichs model
• The spectrum of two-particle bound states for the transfer matrices of Gibbs fields (an isolated bound state)
• Determination of the inertia of a partitioned Hermitian matrix
• Perturbation of a lattice spectral band by a nearby resonance
• L₂-Theory of the Maxwell operator in arbitrary domains
• The Essential Spectrum of Some Matrix Operators
• Random walks in a random (fluctuating) environment
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