Literatur
Ando, T.: Positive linear operators in semi-ordered linear spaces. J. Fac. Sci. Hokkaido Univ. Ser. I.13, 214–228 (1957).
Bachman, G.: Elements of abstract harmonic analysis. New York and London: Academic Press 1964.
Bonsall, F.F., Tomiuk, B.J.: The semi-algebra generated by a compact linear operator. Proc. Edinburgh Math. Soc.14 (S. II), 177–196 (1965).
Dunford, N., Schwartz, J. T.: Linear operators. Part I: General theory. New York: Intersciece Publ. 1958.
Frobenius, G.: Über Matrizen aus positiven Elementen. S.-Ber. Preuss. Akad. Wiss. Berlin1908, 471–476;1909, 514–518.
Frobenius, G.: Über Matrizen aus nicht negativen Elementen, S.-Ber. Press. Akad. Wiss. Berlin1912, 456–477.
Kakutani, S.: Concrete representation of abstract (L)-spaces and the mean ergodic theorem. Ann. of Math. (2)42, 523–537 (1941).
Karlin, S.: Positive operators. J. Math. Mech.8, 907–938 (1959).
Krein, M. G., Rutman, M. A.: Linear operators leaving invariant a cone in a Banach space. Uspehi Mat. Nauk (N. S.)3, No. 1 (23), 3–95 (1948) (Russisch). Auch Amer. Math. Soc. Translat. Ser. 1,10, 199–325 (1962).
Kriger, H.-J.: Beiträge zur Theorie positiver Operatoren. Schriftenreihe der Institute für Mathematik bei der Deutschen Akad. der Wiss. Berlin. Reihe A: Reine Mathematik. Heft6, 1–82 (1969).
Lotz, H. P.: Über das Spektrum positiver Opratoren. Math. Z.108, 15–32 (1968).
—, Schaefer, H. H.: Über einen Satz von F. Niiro und I. Sawashima. Math. Z.108, 33–36 (1968).
Rota, G.-C.: On the eigenvalues of positive operators. Bull. Amer. Math. Soc.67, 556–558 (1961).
Schaefer, H. H.: Topological vector spaces. New York: Macmillan 1966.
—: Convex cones and spectral theory. Proc. Sympos. Pure Math., vol. VII. Convexity, 451–471. Providence, R. I. 1963.
—: Some spectral properties of positive linear operators. Pacific J. Math.10, 1009–1019 (1960).
—: Spektraleigenschaften positiver Operatoren. Math. Z.82, 303–313 (1963).
—: On the point spectrum of positive operators. Proc. Amer. Math. Soc.15, 56–60 (1964).
—: Über das Randspektrum positiver Operatoren. Math. Ann.162, 289–293 (1965).
—: Invariant ideals of positive operators inC(X), I. Illinois J. Math.11, 703–715 (1967).
—: Invariant ideals of positive operators inC(X). II. Illinois J. Math.12, 525–538 (1968).
Taylor, A. E.: Introduction to functional analysis. New York and London: John Wiley & Sons 1958.
Taylor, J. L.: The structure of convolution measure algebras. Trans. Amer. Math. Soc.119, 150–166 (1965).
Wielandt, H.: Unzerlegbare, nicht negative Matrizen. Math. Z.52, 642–648 (1950).
Wolff, M.: Über das Spektrum von Homomorphismen in Banach-Verbänden. Math. Ann.182, 161–169 (1969).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Scheffold, E. Das Spektrum von Verbandsoperatoren in Banachverbänden. Math Z 123, 177–190 (1971). https://doi.org/10.1007/BF01110116
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01110116