Abstract
We prove that ifE is a Banach lattice andS, T ∈ ℒ (E) are such that 0≦s≦T,r(s)=r(T) andr(T) is a Riesz point ofσ(T) thenr(S) is a Riesz point ofσ(S). We prove also some results on compact positive perturbations of positive irreducible operators and lattice homomorphisms.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
C. D. Aliprantis and O. Burkinshaw,Positive compact operators on Banach lattices, Math. Z.174 (1980), 289–298.
J. J. Buoni, R. Harte and T. Wickstead,Upper and lower Fredholm spectra, Proc. Amer. Math. Soc.66 (1977), 309–314.
J. J. M. Chadwick and A. W. Wickstead,A quotient of ultrapowers of Banach spaces and semi-Fredholm operators, Bull. London Math. Soc.9 (1977), 321–325.
R. Derndinger,Uber das Spektrum positiver Generatoren, Math. Z.172 (1980), 281–293.
P. G. Dodds and D. H. Fremlin,Compact operators in Banach lattices, Israel J. Math.34 (1979), 287–320.
G. Greiner,Zur Perron-Frobenius-Theorie stark stetiger Halbgruppen, Math. Z.177 (1981), 401–423.
U. Groh,Uniformly ergodic maps on C*-algebras, Israel J. Math.47 (1984), 227–235.
S. Heinrich,Ultraproducts in Banach space theory, J. Reine Angew. Math.313 (1980), 72–104.
V. I. Istratescu,Introduction to Linear Operator Theory, Pure and Applied Math. Dekker, New York and Basel, 1981.
H. G. Kaper, C. G. Lekkerkerker and J. Hejtmanek,Spectral Methods in Linear Transport Theory, Birkhauser, Basel, 1982.
S. Karlin,Positive operators, J. Math. Mech.8 (1959), 907–937.
A. Lebow and M. Schechter,Semigroups of operators and measures of non-compactness, J. Funct. Anal.7 (1971), 1–26.
J. Lindenstrauss and L. Tzafriri,Classical Banach Spaces I: Sequence Spaces, Springer-Verlag, Berlin-Heidelberg-New York, 1977.
J. Lindenstrauss and L. Tzafriri,Classical Banach Spaces II: Function Spaces, Springer-Verlag, Berlin-Heidelberg-New York, 1979.
U. Moustakas,Majorisierung and Spektraleigenschaften positiver Operatoren auf Banachverbanden, Dissertation, Tubingen, 1984.
B. Pagter,The components of a positive operator, Indag. Math.86 (1983), 229–241.
C. R. Putnam,The spectra of operators having resolvents of first order growth, Trans. Amer. Math. Soc.133 (1968), 505–510.
H. H. Schaefer,Topological Vector Spaces, 3rd print, Springer-Verlag, Berlin-Heidelberg-New York, 1971.
H. H. Schaefer,Banach Lattices and Positive Operators, Springer-Verlag, Berlin-Heidelberg-New York, 1974.
L. Weis and M. P. H. Wolff,On the essential spectrum of operators on L 1,Semesterbericht Funktionalanalysis, Tubingen, Sommersemester 1984.
M. P. H. Wolff,Uber das Spektrum von Verbandshomomorphismen in Banach verbanden, Math. Ann.184 (1969), 49–55.
M. P. H. Wolff,Spectral theory of group representations and their non-standard hull, Israel J. Math.48 (1984), 205–224.
A. C. Zaanen,Riesz Spaces II, North-Holland, Amsterdam, 1983.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Caselles, V. On the peripheral spectrum of positive operators. Israel J. Math. 58, 144–160 (1987). https://doi.org/10.1007/BF02785673
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02785673