On the local spectral radius of positive operators
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- by Mirosława Zima PDF
- Proc. Amer. Math. Soc. 131 (2003), 845-850 Request permission
Abstract:
We give some sufficient conditions for subadditivity and submultiplicativity of the local spectral radius of bounded positive linear operators.References
- Josef Daneš, On local spectral radius, Časopis Pěst. Mat. 112 (1987), no. 2, 177–187 (English, with Russian and Czech summaries). MR 897643
- A.R.Esayan, On the estimation of the spectral radius of the sum of positive semicommutative operators (in Russian), Sibirsk. Math. Zh. 7 (1966), 460–464.
- K.-H. Förster and B. Nagy, On the local spectral theory of positive operators, Special classes of linear operators and other topics (Bucharest, 1986) Oper. Theory Adv. Appl., vol. 28, Birkhäuser, Basel, 1988, pp. 71–81. MR 942914
- K.-H. Förster and B. Nagy, On the local spectral radius of a nonnegative element with respect to an irreducible operator, Acta Sci. Math. (Szeged) 55 (1991), no. 1-2, 155–166. MR 1124954
- M. A. Krasnosel′skiĭ, G. M. Vaĭnikko, P. P. Zabreĭko, Ya. B. Rutitskii, and V. Ya. Stetsenko, Approximate solution of operator equations, Wolters-Noordhoff Publishing, Groningen, 1972. Translated from the Russian by D. Louvish. MR 0385655
- Kjeld B. Laursen and Michael M. Neumann, An introduction to local spectral theory, London Mathematical Society Monographs. New Series, vol. 20, The Clarendon Press, Oxford University Press, New York, 2000. MR 1747914
- Vladimír Müller, Local spectral radius formula for operators in Banach spaces, Czechoslovak Math. J. 38(113) (1988), no. 4, 726–729. MR 962915
- Saunders MacLane, Steinitz field towers for modular fields, Trans. Amer. Math. Soc. 46 (1939), 23–45. MR 17, DOI 10.1090/S0002-9947-1939-0000017-3
- M. Zima, A theorem on the spectral radius of the sum of two operators and its application, Bull. Austral. Math. Soc. 48 (1993), no. 3, 427–434. MR 1248046, DOI 10.1017/S0004972700015884
- Mirosława Zima, On the local spectral radius in partially ordered Banach spaces, Czechoslovak Math. J. 49(124) (1999), no. 4, 835–841. MR 1746709, DOI 10.1023/A:1022413403733
Additional Information
- Mirosława Zima
- Affiliation: Institute of Mathematics, University of Rzeszów, Rejtana 16 A, 35-310 Rzeszów, Poland
- Email: mzima@univ.rzeszow.pl
- Received by editor(s): July 6, 2001
- Received by editor(s) in revised form: October 15, 2001
- Published electronically: July 2, 2002
- Communicated by: David R. Larson
- © Copyright 2002 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 131 (2003), 845-850
- MSC (2000): Primary 47A11, 47B65
- DOI: https://doi.org/10.1090/S0002-9939-02-06726-6
- MathSciNet review: 1937422