On the local spectral radius of positive operators

Author:
Miroslawa 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

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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.

**1.**J.Danes,*On local spectral radius*, Cas. pest. mat.**112**(1987), 177-187. MR**88j:47004****2.**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.**3.**K.H.Förster and B.Nagy,*On the local spectral theory of positive operators*, Operator Theory: Advances and Applications, vol. 28, Birkhäuser, Basel, 1988, pp. 71-81. MR**89g:47049****4.**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**(1991), 155-166. MR**92j:47016****5.**M.A.Krasnoselskii et al.,*Approximate solutions of operator equations*, Noordhoff, Groningen, 1972. MR**52:6515****6.**K.B.Laursen and M.M.Neumann,*Introduction to local spectral theory,*Lond. Math. Soc. Monographs, Oxford Univ. Press, 2000. MR**2001k:47002****7.**V.Müller,*Local spectral radius formula for operators in Banach spaces*, Czechoslovak Math. J.**38**(1988), 726-729. MR**89g:47005****8.**F.Riesz and B.Sz.-Nagy,*Functional analysis*, Ungar, New York, 1955. MR**17:175i****9.**M.Zima,*A theorem on the spectral radius of the sum of two operators and its applications*, Bull. Austral. Math. Soc.**48**(1993), 427-434. MR**94j:47006****10.**M.Zima,*On the local spectral radius in partially ordered Banach spaces*, Czechoslovak Math. J.**49**(1999), 835-841. MR**2001m:47011**

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Additional Information

**Miroslawa Zima**

Affiliation:
Institute of Mathematics, University of Rzeszów, Rejtana 16 A, 35-310 Rzeszów, Poland

Email:
mzima@univ.rzeszow.pl

DOI:
https://doi.org/10.1090/S0002-9939-02-06726-6

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

Article copyright:
© Copyright 2002
American Mathematical Society