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Journal of the London Mathematical Society Advance Access originally published online on January 12, 2007
Journal of the London Mathematical Society 2007 75(1):35-46; doi:10.1112/jlms/jdl004
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© 2007 London Mathematical Society

One-sided ideals and right cancellation in the second dual of the group algebra and similar algebras

Mahmoud Filali and Pekka Salmi

Department of Mathematical Sciences
University of Oulu
PL 3000
90014 Oulun Yliopisto
Finland
mahmoud.filali{at}oulu.fi
pekka.salmi{at}oulu.fi

The following results are proved for a non-compact, locally compact group G: the dimension of every non-trivial right ideal in L1(G)** (equipped with the first Arens product) is at least Formula , where {kappa}(G) is the minimal number of compact sets required to cover G; there exist Formula left ideals in L1(G)** and in LUC(G)* with trivial intersections, and the linear span of right-cancellable elements is weak*-dense in the annihilator of C0(G) in LUC(G)* and in the annihilator of Formula (the L{infty}-functions that vanish at infinity) in L{infty}(G)*. The same results are proved for weighted algebras when the weight function is diagonally bounded.

2000 Mathematics Subject Classification 43A20 (primary), 22D15, 22A15 (secondary).

Received June 16, 2004; revised July 11, 2005; published online January 12, 2007.


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