Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


A characterization of the Leinert property
HTML articles powered by AMS MathViewer

by Franz Lehner PDF
Proc. Amer. Math. Soc. 125 (1997), 3423-3431 Request permission


Let $G$ be a discrete group and denote by $\lambda _G$ its left regular representation on $\ell _2(G)$. Denote further by $\mathbf {F}_n$ the free group on $n$ generators $\{g_1,g_2,\ldots ,g_n\}$ and $\lambda$ its left regular representation. In this paper we show that a subset $S=\{ t_1, t_2, \ldots , t_n \}$ of $G$ has the Leinert property if and only if for some real positive coefficients $\alpha _1,\alpha _2,\ldots ,\alpha _n$ the identity \[ \biggl \| \sum _{i=1}^n \alpha _i \lambda _G(t_i) \biggr \|_{C_\lambda ^*(G)} = \biggl \| \sum _{i=1}^n \alpha _i \lambda (g_i) \biggr \|_{C_\lambda ^*(\mathbf {F}_n)} \] holds. Using the same method we obtain some metric estimates about abstract unitaries $U_1,U_2,\ldots , U_n$ satisfying the similar identity $\biggl \|\sum _{i=1}^n U_i \otimes \overline {U_i}\biggr \|_{\min }$$=2\sqrt {n-1}.$
Similar Articles
Additional Information
  • Franz Lehner
  • Affiliation: Institut für Mathematik, Johannes Kepler Universität Linz, A4040 Linz, Austria
  • Address at time of publication: IMADA, Odense Universitet, Campusvej 55, DK 5230 Odense M, Denmark
  • Email:,
  • Received by editor(s): February 22, 1996
  • Received by editor(s) in revised form: May 21, 1996
  • Communicated by: Palle E. T. Jorgensen
  • © Copyright 1997 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 125 (1997), 3423-3431
  • MSC (1991): Primary 22D25; Secondary 43A05, 43A15, 60J15
  • DOI:
  • MathSciNet review: 1402870