Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

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

 
 

 

Finite-dimensional invariant subspace property and amenability for a class of Banach algebras


Authors: Anthony To-Ming Lau and Yong Zhang
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
Published electronically: July 1, 2015
MathSciNet review: 3453356
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2010): 46H20, 43A20, 43A10, 46H25, 16E40

Retrieve articles in all journals with MSC (2010): 46H20, 43A20, 43A10, 46H25, 16E40


Additional Information

Anthony To-Ming Lau
Affiliation: Department of Mathematical and Statistical sciences, University of Alberta, Edmonton, Alberta, T6G 2G1 Canada
Email: tlau@math.ualberta.ca

Yong Zhang
Affiliation: Department of Mathematics, University of Manitoba, Winnipeg, Manitoba, R3T 2N2 Canada
Email: zhangy@cc.umanitoba.ca

DOI: https://doi.org/10.1090/tran/6442
Keywords: Fixed point property, invariant mean, finite invariant subspace, F-algebra, quantum group, Hopf von Neumann algebra, ideal, module morphism
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
Article copyright: © Copyright 2015 American Mathematical Society

American Mathematical Society