Abstract
This expository note is devoted to a discussion of the equivalence of inertia theorems of the Carlson–Schneider type with the existence of finitedimensional reproducing kernel Krein spaces of the de Branges type. The first five sections focus on an inertia theorem connected with a Lyapunov equation. A sixth supplementary section sketches an analogous treatment of the Stein equation. The topic was motivated by a question raised by Leonid Lerer.
Mathematics Subject Classification (2010). 46C20, 46E22, 47B32, 47B50, 93B20.
To Leonid Lerer on the occasion of his retirement from the faculty of the Department of Mathematics at the Technion, with affection and respect.
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Dym, H., Porat, M. (2013). Long Proofs of Two Carlson–Schneider Type Inertia Theorems. In: Kaashoek, M., Rodman, L., Woerdeman, H. (eds) Advances in Structured Operator Theory and Related Areas. Operator Theory: Advances and Applications, vol 237. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0639-8_9
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