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Limiting set of second order spectra
Let $M$ be a self-adjoint operator acting on a Hilbert space $\mathcal {H}$. A complex number $z$ is in the second order spectrum of $M$ relative to a finite-dimensional subspace $\mathcal {L}\subset \operatorname {Dom} M^2$ iff the truncation to $\mathcal {L}$ of $(M-z)^2$ is not invertible. This definition was first …