Annals of Functional Analysis

Commuting contractive idempotents in measure algebras

Nico Spronk

Full-text: Access denied (no subscription detected) We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

We determine when contractive idempotents in the measure algebra of a locally compact group commute. We consider a dynamical version of the same result. We also look at some properties of groups of measures whose identity is a contractive idempotent.

Article information

Source
Ann. Funct. Anal. Volume 7, Number 1 (2016), 136-149.

Dates
Received: 15 March 2015
Accepted: 11 August 2015
First available in Project Euclid: 22 December 2015

Permanent link to this document
https://projecteuclid.org/euclid.afa/1450803721

Digital Object Identifier
doi:10.1215/20088752-3428247

Mathematical Reviews number (MathSciNet)
MR3449346

Zentralblatt MATH identifier
1334.43001

Subjects
Primary: 43A05: Measures on groups and semigroups, etc.
Secondary: 43A77: Analysis on general compact groups 43A40: Character groups and dual objects

Keywords
measure algebra idempotent groups of measures

Citation

Spronk, Nico. Commuting contractive idempotents in measure algebras. Ann. Funct. Anal. 7 (2016), no. 1, 136--149. doi:10.1215/20088752-3428247. https://projecteuclid.org/euclid.afa/1450803721.


Export citation

References

  • [1] P. J. Cohen, On a conjecture of Littlewood and idempotent measures, Amer. J. Math. 82 (1960), 191–212.
  • [2] F. P. Greenleaf, Norm decreasing homomorphisms of group algebras, Pacific J. Math. 15 (1965), 1187–1219.
  • [3] Y. Kawada and K. Itô, On the probability distribution on a compact group, I, Proc. Phys.-Math. Soc. Japan (3) 22 (1940), 977–998.
  • [4] A. Mukherjea, Idempotent probabilities on semigroups, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 11 (1969), 142–146.
  • [5] M. Neufang, P. Salmi, A. Skalski, and N. Spronk, Contractive idempotents on locally compact quantum groups, Indiana Univ. Math. J. 62 (2013), no. 6, 1983–2002.
  • [6] T. W. Palmer, Banach Algebras and the General Theory of $*$-Algebras, Vol. 2: $*$-Algebras. Cambridge Univ. Press, Cambridge, 2001.
  • [7] D. Rider, Central idempotent measures on compact groups, Trans. Amer. Math. Soc. 186 (1973), 459–479.
  • [8] W. Rudin, Fourier Analysis on Groups. Wiley, New York, 1990.
  • [9] R. Stokke, Homomorphisms of convolution algebras, J. Funct. Anal. 261 (2011), no. 12, 3665–3695.
  • [10] K. Stromberg, Probabilities on a compact group, Trans. Amer. Math. Soc. 94 (1960) 295–309.
  • [11] J. Szép, Über die als Produkt zweier Untergruppen darstellbaren endlichen Gruppen, Comment. Math. Helv. 22 (1949), 31–33.
  • [12] M. Takeuchi, Matched pairs of groups and bismash products of Hopf algebras, Comm. Algebra 9 (1981), no. 8, 841–882.
  • [13] N. J. Young The irregularity of multiplication in group algebras, Quart. J. Math. Oxford Ser. (2) 24 (1973), 59–62.
  • [14] G. Zappa, “Sulla costruzione dei gruppi prodotto di due dati sottogruppi permutabili tra loro” in Atti Secondo Congresso Un. Mat. Ital. (Bologna, 1940), Edizioni Cremonense, Rome, 1942, 119–125.