ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

8. Analysis

1991 MS Classification: 43A45, 46J10 Salinger, David L., University of Leeds, England and Stegeman, J. D. , Rijksuniversiteit Utrecht, Netherlands Lifting the Difference Spectrum In the Banach algebra A(G), where G is a non-discrete locally compact abelian group and A(G) denotes the Gelfand-Fourier transform of L^{1}(Ĝ), it is well-known that there are closed subsets E ⊂ G which are the hulls of distinct closed ideals. Denote the largest such ideal by I(E) and the smallest by J(E). For such sets of non-synthesis E, we can investigate the difference spectrum Δ(E) := {x ∈ E : ∃f ∈ I(E) such that there is no neighbourhood U of x on which f coincides with a function in J(E) }. In [1] it was shown that every non-metrizable G contains E such that Δ(E) is not closed. We discuss this and the related question whether Δ(π^{−1}(E)) = π^{−1}(Δ(E)) for a surjective homomorphism π : H → G.

[1] D. L. Salinger and J. D. Stegeman, Difference spectra of ideals for nonmetrizable groups, J. London Math. Soc. (2), 26 (1982), 531-540.