Proceedings of the American Mathematical Society

Uniformly complete quotient space

and completely isometric representations of

on $\mathcal{B}(L_2(G))$

Author(s): Ana-Maria Popa; Zhong-Jin Ruan
Journal: Proc. Amer. Math. Soc. 134 (2006), 1223-1235.
MSC (2000): Primary 22D15, 22D20, 43A22, 46L07, 47L10
Posted: October 18, 2005
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Abstract: The uniformly complete quotient space

of a locally compact group

is introduced. It is shown that the operator space dual

is a completely contractive Banach algebra, which contains the completely bounded Fourier multiplier algebra $M_{cb}A(G)$ as a completely contractively complemented Banach subalgebra. A natural completely isometric representation of

on $\mathcal{B}(L_2(G))$ is studied and some equivalent amenability conditions associated with

are proved.

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Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 22D15, 22D20, 43A22, 46L07, 47L10

Ana-Maria Popa
Affiliation: Department of Mathematics, University of Illinois, Urbana, Illinois 61801
Email: popa@math.uiuc.edu

Zhong-Jin Ruan
Affiliation: Department of Mathematics, University of Illinois, Urbana, Illinois 61801
Email: ruan@math.uiuc.edu

DOI: 10.1090/S0002-9939-05-08075-5
PII: S 0002-9939(05)08075-5
Received by editor(s): July 28, 2004
Received by editor(s) in revised form: November 8, 2004
Posted: October 18, 2005
Additional Notes: The second author was partially supported by the National Science Foundation DMS-0140067
Communicated by: David R. Larson
Copyright of article: Copyright 2005, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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