On the local spectral radius of positive operators

Zima, Mirosława

doi:10.1090/S0002-9939-02-06726-6

On the local spectral radius of positive operators

Author: Mirosława Zima
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
Published electronically: July 2, 2002
MathSciNet review: 1937422
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We give some sufficient conditions for subadditivity and submultiplicativity of the local spectral radius of bounded positive linear operators.

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

F.Riesz and B.Sz.-Nagy, Functional analysis, Ungar, New York, 1955.

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 https://doi.org/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 https://doi.org/10.1023/A%3A1022413403733