A new concept for block operator matrices:The quadratic numerical range

Linear Algebra and Its Applications

Volumn 330, Issue 1-3, 2001, Pages 89-112

  Langer, H ^a   Markus, A ^b   Matsaev, V ^c   Tretter, C ^d  

^a VIENNA UNIVERSITY OF TECHNOLOGY   (Austria)

^b BEN GURION UNIVERSITY OF THE NEGEV   (Israel)

^c TEL AVIV UNIVERSITY   (Israel)

^d UNIVERSITY OF LEICESTER   (United Kingdom)

Author keywords

Angular operator; Block operator matrix; Quadratic numerical range; Riccati equation; Schur complement

Indexed keywords

EID: 0035877008     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0024-3795(01)00230-0     Document Type: Article

References (14)

1. Adamjan V.M., Langer H. Spectral properties of a class of rational operator valued functions. J. Operator Theory. 33:1995;259-277.
2. J.M. Ayerbe Toledano, T. Dominguez Benavides, G. López Acedo, Measures of Noncompactness in Metric Fixed Point Theory, Operator Theory: Adv. Appl. 99, Birkhäuser, Basel, 1997.
3. Daleckii Ju.L., Krein M.G. Stability of Solutions of Differential Equations in Banach Space. AMS Transl. Math. Monographs. 43:1974.
4. I.C. Gohberg, S. Goldberg, M.A. Kaashoek, Classes of Linear Operators, vol. I, Operator Theory: Adv. Appl. 49, Birkhäuser, Basel, 1990.
5. Gustafson K.E., Rao D.K.M. Numerical Range. 1997;Springer, Berlin.
6. Halmos P.R. A Hilbert Space Problem Book. second ed. 1982;Springer, Berlin.
7. Hurwitz A., Courant R. Funktionentheorie. 1964;Springer, Berlin.
8. Krupnik N., Markus A.S., Matsaev V. Factorization of matrix functions and characteristic properties of the circle. Integral Equations Operator Theory. 17(4):1993;554-566.
9. Langer H., Tretter C. Spectral decomposition of some nonselfadjoint block operator matrices. J. Operator Theory. 39:1998;339-359.
10. Langer H., Tretter C. Diagonalization of certain block operator matrices and applications to Dirac operators. Operator Theory: Adv. Appl. 122:2001;331-358.
11. H. Langer, A.S. Markus, C. Tretter, Corners of numerical ranges, Operator Theory: Adv. Appl. 124 (2001) 385-400.
12. Markus A.S. Introduction to the Theory of Polynomial Operator Pencils. AMS Transl. Math. Monographs. 71:1988.
13. Markus A.S., Matsaev V. On the spectral theory of holomorphic operator-valued functions in Hilbert space. Funct. Anal. Appl. 9(1):1975;73-74.
14. Mennicken R., Shkalikov A.A. Spectral decomposition of symmetric operator matrices. Math. Nachr. 179:1996;259-273.