A linearization for operator polynomials with coefficients in certain operator ideals
- 29 Downloads
For an operator polynomial with coefficients in certain Von Neumann-Schatten classes a linearization is constructed. The linearization also belongs to a Von Neumann-Schatten class, and its regularized Fredholm determinant determines the spectral properties of the original polynomial.
KeywordsSpectral Property Operator Ideal Fredholm Determinant Operator Polynomial Original Polynomial
Unable to display preview. Download preview PDF.
- N. Dunford -J. T. Schwartz,Linear operators, Part II, Interscience, New York, 1963.Google Scholar
- I. Gohberg -M. A. Kaashoek -D. C. Lay,Equivalence, linearization and decomposition of holomorphic opefator functions, J. Functional Anal.,28 (1) (1978), pp. 102–142.Google Scholar
- I. C. Gohberg -M. G. Krein,Introduction to the theory of linear nonselfadjoint operators, Translations of mathematical monographs, vol. 18, American Mathematical Society, Providence, 1968.Google Scholar
- N. A. Kulesko -Ju. A. Palant,On a theorem of E. I. Sigal about the trace of an operator bundle, Mat. Issled 6, vyp 2 (1971), pp. 150–152 (Russian).Google Scholar
- A. V. Laginestra -W. E. Boyce,Convergence and evaluation of reciprocal powers of eigenvalues of certain compact operators (on Hilbert space) which are meromorphic functions of the eigenvalue parameter, Ann. Mat. pura appl., IV Ser.,111 (1975), pp. 229–305.Google Scholar
- E. I. Sigal,On the trace of an operator bundle, Mat. Issled 4, vyp 2 (1969), pp. 148–151 (Russian).Google Scholar