Annals of Functional Analysis

Commuting contractive idempotents in measure algebras

Nico Spronk

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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

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

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

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

measure algebra idempotent groups of measures


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

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  • [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.