Vol. 141, No. 2, 1990

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 300: 1  2
Vol. 299: 1  2
Vol. 298: 1  2
Vol. 297: 1  2
Vol. 296: 1  2
Vol. 295: 1  2
Vol. 294: 1  2
Vol. 293: 1  2
Online Archive
The Journal
Editorial Board
Special Issues
Submission Guidelines
Submission Form
Author Index
To Appear
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Other MSP Journals
Complementation of certain subspaces of Lāˆž(G) of a locally compact group

Anthony To-Ming Lau and Viktor Losert

Vol. 141 (1990), No. 2, 295ā€“310

Let G be a locally compact group, WAP(G) be the space of continuous weakly almost periodic functions on G and C0(G) the space of continuous functions on G vanishing at infinity. We prove in this paper, among other things, that if G is infinite and X is any subspace of WAP(G) (or CB(G), the space of bounded continuous functions in case G is nondiscrete) containing C0(G), then X is uncomplemented in L(G). If G is non-compact, then WAP(G) is uncomplemented in LUC(G). Furthermore, AP(G), the space of continuous almost periodic functions on G, is complemented in LUC(G) if and only if G∕N is compact, where N is the intersection of the kernels of all finite-dimensional continuous unitary representations of G. We also prove that if A is any left translation invariant C-subalgebra of C0(G), then A is the range of a continuous projection commuting with left translations.

Mathematical Subject Classification 2000
Primary: 43A60
Secondary: 22D15
Received: 29 September 1987
Revised: 18 September 1988
Published: 1 February 1990
Anthony To-Ming Lau
Viktor Losert