engleski

On quasi-definite quadratic forms in a Hilbert space

We present a perturbation theory for sign-indefinite quadratic forms in a Hilbert space. We specifically allow forms which are unbounded at both ends. Under an additional qualitative assumption on the structure of the form, which is in analogy to the structure of the so called quasi-definite matrices form Linear Algebra, we prove an operator representation theorem for those quadratic forms. Furthermore, with the help of weakly formulated Riccati equations we obtain subspace perturbation theorems for such operators and present accompanying estimates on the perturbation of the spectra. The example of the Stokes block matrix operator---which is associated to the Cosserat eigenvalue problem---is used to illustrate our theory and to show that our estimates can be attained. This is a joint work with V. Kostrykin, K. A. Makarov and K. Veselić.

indefinite quadratic forms; Hilbert space

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