Skip to Main Content

Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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.

 

Finite-dimensional invariant subspace property and amenability for a class of Banach algebras
HTML articles powered by AMS MathViewer

by Anthony To-Ming Lau and Yong Zhang PDF
Trans. Amer. Math. Soc. 368 (2016), 3755-3775 Request permission

Abstract:

Motivated by a result of Ky Fan in 1965, we establish a characterization of a left amenable F-algebra (which includes the group algebra and the Fourier algebra of a locally compact group and quantum group algebras, or more generally the predual algebra of a Hopf von Neumann algebra) in terms of a finite-dimensional invariant subspace property. This is done by first revealing a fixed point property for the semigroup of norm one positive linear functionals in the algebra. Our result answers an open question posted in Tokyo in 1993 by the first author. We also show that the left amenability of an ideal in an F-algebra may determine the left amenability of the algebra.
References
Similar Articles
Additional Information
  • Anthony To-Ming Lau
  • Affiliation: Department of Mathematical and Statistical sciences, University of Alberta, Edmonton, Alberta, T6G 2G1 Canada
  • MR Author ID: 110640
  • Email: tlau@math.ualberta.ca
  • Yong Zhang
  • Affiliation: Department of Mathematics, University of Manitoba, Winnipeg, Manitoba, R3T 2N2 Canada
  • ORCID: 0000-0002-0440-6396
  • Email: zhangy@cc.umanitoba.ca
  • Received by editor(s): May 31, 2013
  • Received by editor(s) in revised form: March 5, 2014
  • Published electronically: July 1, 2015
  • Additional Notes: The first author was supported by NSERC Grant MS100
    The second author was supported by NSERC Grant 238949
  • © Copyright 2015 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 368 (2016), 3755-3775
  • MSC (2010): Primary 46H20, 43A20, 43A10; Secondary 46H25, 16E40
  • DOI: https://doi.org/10.1090/tran/6442
  • MathSciNet review: 3453356