ReferenceLiteratur
Alaoglu, L., andG. Birkhoff: General ergodic theorems. Ann. of Math.41, 293–309 (1940).
Birkhoff, G.: An ergodic theorem for general semigroups. Proc. Nat. Acad. Sci. U. S. A.25, 625–627 (1939).
Bourbaki, N.: Espaces vectoriels topologiques. Paris 1953.
Day, M. M.: Reflexive spaces not isomorphic to uniformly convex spaces. Bull. Amer. Math. Soc.47, 313–317 (1941).
Day, M. M.: Ergodic theorems for abelian semigroups. Trans. Amer. Math. Soc.51, 399–412 (1942).
Day, M. M.: Uniform convexity in factor and conjugate spaces. Ann. of Math.45, 375–385 (1944).
Day, M. M.: Means for the bounded functions and ergodicity of the bounded representations of semi-groups. Trans. Amer. Math. Soc.69, 276–291 (1950).
Dunford, N., andS. Miller: On the ergodic theorem. Trans. Amer. Math. Soc.60, 538–549 (1946).
Eberlein, W. F.: Abstract ergodic theorems and weakly almost periodic functions. Trans. Amer. Math. Soc.67, 217–250 (1949).
Godement, R.: Les fonctions de type positif et la théorie des groupes. Trans. Amer. Math. Soc.63, 1–84 (1948).
Jacobs, K.: Periodizitätseigenschaften beschränkter Gruppen im Hilbertschen Raum. Math. Z.61, 408–428 (1955).
Jacobs, K.: Ergodentheorie und fastperiodische Funktionen auf Halbgruppen. Math. Z.64, 298–338 (1956).
Keiner, H.: Verallgemeinerte fastperiodische Funktionen anf Halbgruppen. Arch. Math. 1957.
Lorch, E. R.: Means of iterated transformations in reflexive vector spaces. Bull. Amer. Math. Soc.45, 945–947 (1939).
Maak, W.: Fastperiodische Funktionen auf Halbgruppen. Acta mathematica87, 33–57 (1952).
Maak, W.: Integralmittelwerte von Funktionen auf Gruppen und Halbgruppen. J. reine u. angew. Math.190, 34–48 (1952).
Sz.-Nagy, B.: Spektraldarstellungen linearer Transformationen des Hilbertschen Raumes. Berlin 1942.
Pettis: A proof that every uniformly convex space is reflexive. Duke Math. J.5, 249–253 (1939).
Riesz, F.: Some mean ergodic theorems. J. London Math. Soc.13, 274–278 (1938).
Riesz, F.: Sur la théorie ergodique des espaces abstraits. Acta Sci. Math. Szeged10, 1–20 (1941).
Riesz, F.: Another proof of the mean ergodic theorem. Acta Sci. Math. Szeged10, 75–76 (1941).
Riesz, F., u.B. Sz.-Nagy: Lecons d'analyse fonctionnelle. Budapest 1952.
Yosida, K., andS. Kakutani: Operator-theoretical treatment of Markoff process and mean ergodic theorem. Ann. of Math.42, 188–228 (1941).
Dixmier, J.: Les moyennes invariantes daus les semi-groupes et leurs applications. Acta Sci. Math. Szeged12, 213–227 (1950).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Jacobs, K. Fastperiodizitätseigenschaften allgemeiner Halbgruppen in Banach-Räumen. Math Z 67, 83–92 (1957). https://doi.org/10.1007/BF01258845
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01258845