Averaging theorems for linear operators in compact groups and semigroups

• Autorzy: G. J. Murphy , T. T. West
• Języki publikacji: EN

Abstrakty

EN

The Weyl criterion for uniform distribution of a sequence has an especially simple form in compact abelian groups. The authors use this and the structure of compact monothetic groups and semigroups to generalise the convergence, under certain compactness conditions, of the operator averages: $n^{-1} ∑_{k=1}^n T^k → P (n→ ∞)$ where P is a projection associated with the eigenvalue one of T.

Kategorie tematyczne

• 47A35: Ergodic theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1997
• Tom: 124
• Numer: 3
• Strony: 249-258

Daty

wydano

1997

otrzymano

1996-02-20

poprawiono

1997-01-08

Twórcy

autor

G. J. Murphy

• Department of Mathematics, University College, Cork, Ireland

autor

T. T. West

• School of Mathematics, Trinity College, Dublin, Ireland

Bibliografia

• [1] G. Brown and W. Moran, Idempotents of compact monothetic semigroups, Proc. London Math. Soc. 22 (1971), 203-216.
• [2] G. Brown and W. Moran, An unusual compact monothetic semigroup, Bull. London Math. Soc. 3 (1971), 291-296.
• [3] B. Eckmann, Über monothetische Gruppen, Comment. Math. Helv. 16 (1944), 249-263.
• [4] T. A. Gillespie and T. T. West, Operators generating weakly compact groups, Indiana Univ. Math. J. 21 (1972), 671-688.
• [5] E. Hlawka, The Theory of Uniform Distribution, A B Academic Publishers, Berkhamsted, Herts, 1984.
• [6] M. A. Kaashoek and T. T. West, Locally compact monothetic semi-algebras, Proc. London Math. Soc. 18 (1968), 428-438.
• [7] K. de Leeuw and I. Glicksberg, Applications of almost periodic compactifications, Acta Math. 105 (1961), 63-97.
• [8] W. Rudin, Fourier Analysis on Groups, Interscience, New York, 1962.
• [9] T. T. West, Weakly compact monothetic semigroups of operators in Banach spaces, Proc. Roy. Irish Acad. Sect. A 67 (1968), 27-37.