Local spectral radii and Collatz-Wielandt numbers of monic operator polynomials with nonnegative coefficients

Linear Algebra and Its Applications

Volumn 268, Issue 1-3, 1998, Pages 41-57

  Forster K H ^a   Nagy, B ^b  

^a TECHNISCHE UNIVERSITÄT BERLIN   (Germany)

^b BUDAPEST UNIVERSITY OF TECHNOLOGY AND ECONOMICS   (Hungary)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0042855310     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0024-3795(97)89323-8     Document Type: Article

References (20)

1. I. Colojoara and C. Foias, Theory of Generalized Spectral Operators, Gordon and Breach, New York, 1968.
2. N. Dunford and J. T. Schwartz, Linear Operators, Part III: Spectral Operators, Wiley-Interscience, New York, 1971.
3. L. Elsner, M. Neumann, and B. Vernmer, The effect of the number of processors on the convergence rate to the parallel block Jacobi method, Linear Algebra Appl. 154-156:311-360 (1991).
4. K.-H. Förster and B. Nagy, On the local spectral theory of positive operators, in Oper. Theory Adv. Appl. 28, Birkhäuser, Basel, 1988, pp. 71-81.
5. K.-H. Förster and B. Nagy, On the Collatz-Wielandt numbers and the local spectral radius of a nonnegative operator, Linear Algebra Appl. 120:193-205 (1989).
6. K.-H. Förster and B. Nagy, Some properties of the spectral radius of a monic operator polynomial with nonnegative compact coefficients, Integral Equations Operator Theory 14:794-805 (1991).
7. K.-H. Förster and B. Nagy, On the local spectral radius of a nonnegative element with respect to an irreducible operator, Acta Sci. Math. 55:155-166 (1991).
8. K.-H. Förster and B. Nagy, Spektraleigenschaften von Matrix- und Operatorpolynomen, Sitzungsber. Berliner Math. Ges., Berlin, 1994.
9. S. Friedland and H. Schneider, The growth of powers of a nonnegative matrix, SIAM J. Algebraic Discrete Methods 1:185-200 (1980).
10. K. P. Hadeler, Eigenwerte von Operatorpolynomen, Arch. Rational Mech. Appl. 20:72-80 (1965).
11. B. A. Ivanov, Variational spectral properties of nonnegative operator functions (in Russian), Sibirsk. Mat. Zh. 26(5):86-93 (1985).
12. M. A. Krasnosel'skii, Positive Solutions of Operator Equations, Noordhoff, Groningen, 1964.
13. K. B. Laursen and M. Neumann, Local spectral theory and spectral inclusions, Preprint, Københavns Univ., Mat. Inst., (1993).
14. I. Marek, On the polynomial eigenvalue problem with positive operators and location of the spectral radius, Apl. Mat. 14:146-159 (1969).
15. I. Marek, Collatz-Wielandt numbers in general partially ordered spaces, Linear Algebra Appl. 173:165-180 (1992).
16. P. Meyer-Nieberg, Banach Lattices, Springer-Verlag, New York, 1991.
17. I. Marek and R. S. Varga, Nested bounds for the spectral radius, Numer. Math. 14:49-70 (1970).
18. T. P. Rau, On the peripheral spectrum of a monic operator polynomial with positive coefficients, Integral Equations Operator Theory 15:479-495 (1992).
19. L. Rodman, An Introduction to Operator Polynomials, OT 38, Birkhäuser, Basel, 1989.
20. H. H. Schaefer, Topological Vector Spaces, Springer-Verlag, New York, 1971.