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A new concept for block operator matrices:the quadratic numerical range |
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| Authors: | H. Langer A. Markus V. Matsaev C. Tretter |
| Affiliation: | a Institut für Analysis und Technische Mathematik, Technische Universität Wien, A-1040 Wien, Austria b Department of Mathematics, Ben-Gurion University of the Negev, Beer Sheva 84105, Israel c School of Mathematical Sciences, Tel Aviv University, Ramat Aviv 69978, Israel d Department of Mathematics and Computer Science, University of Leicester, Leicester LE1 7RH, UK |
| Abstract: | In this paper a new concept for 2×2-block operator matrices – the quadratic numerical range – is studied. The main results are a spectral inclusion theorem, an estimate of the resolvent in terms of the quadratic numerical range, factorization theorems for the Schur complements, and a theorem about angular operator representations of spectral invariant subspaces which implies e.g. the existence of solutions of the corresponding Riccati equations and a block diagonalization. All results are new in the operator as well as in the matrix case. |
| Keywords: | Block operator matrix Quadratic numerical range Schur complement Angular operator Riccati equation |
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