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On the local spectral radius in partially ordered Banach spaces. (English) Zbl 1008.47004

The paper studies subadditivity and submultiplicativity of the local spectral radius of operators in partially ordered Banach spaces. The results are then applied to show the uniqueness of solutions of certain differential-functional equations of neutral type.

MSC:

47A11 Local spectral properties of linear operators
37K40 Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems
47B60 Linear operators on ordered spaces
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References:

[1] A. Augustynowicz, M. Kwapisz: On a numerical-analytic method of solving of boundary value problem for functional differential equation of neutral type. Math. Nachr. 145 (1990), 255-269. · Zbl 0762.65046 · doi:10.1002/mana.19901450120
[2] J. Banaś: Applications of measures of noncompactness to various problems. Folia Scientiarum Universitatis Technicae Resoviensis 34 (1987). · Zbl 0619.47044
[3] D. Bugajewski: On some applications of theorems on the spectral radius to differential equations. J. Anal. Appl. 16 (1997), 479-484. · Zbl 0880.35125 · doi:10.4171/ZAA/774
[4] D. Bugajewski, M. Zima: On the Darboux problem of neutral type. Bull. Austral. Math. Soc. 54 (1996), 451-458. · Zbl 0879.35108 · doi:10.1017/S0004972700021869
[5] J. Daneš: On local spectral radius. Čas. pěst. mat. 112 (1987), 177-187. · Zbl 0645.47002
[6] A. R. Esayan: On the estimation of the spectral radius of the sum of positive semicommutative operators (in Russian). Sib. Mat. Zhur. 7, 460-464.
[7] L. Faina: Existence and continuous dependence for a class of neutral functional differential equations. Ann. Polon. Math. 64 (1996), 215-226. · Zbl 0873.34051
[8] K.-H. Förster, B. Nagy: On the local spectral radius of a nonnegative element with respect to an irreducible operator. Acta Sci. Math. 55 (1991), 155-166. · Zbl 0757.47002
[9] M. A. Krasnoselski et al.: Approximate solutions of operator equations. Noordhoff, Groningen, 1972.
[10] V. Müller: Local spectral radius formula for operators in Banach spaces. Czechoslovak Math. J. 38 (1988), 726-729. · Zbl 0707.47005
[11] P. P. Zabrejko: The contraction mapping principle in K-metric and locally convex spaces (in Russian). Dokl. Akad. Nauk BSSR 34 (1990), 1065-1068. · Zbl 0722.47044
[12] M. Zima: A certain fixed point theorem and its applications to integral-functional equations. Bull. Austral. Math. Soc. 46 (1992), 179-186. · Zbl 0761.34048 · doi:10.1017/S0004972700011813
[13] 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. · Zbl 0795.34069 · doi:10.1017/S0004972700015884
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