ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

8. Analysis

1991 MS Classification: 43, 46, 15 Assiamoua, V. S. Kofi, Université du Bénin, Lomé, Togo A product of sesquilinear mappings on Hilbert spaces Let G be a compact group, Σ its dual object, H_{σ} the representation Hilbert space of dimension n_{σ} of σ s elements, σ ∈ Σ and A a complex Banach algebra. In (*), we proved that for every L_{1}(G, A) - multiplier T, there exists a family (Θ_{σ})_{σ∈Σ} of bounded sesquilinear mappings Θ_{σ} : H_{σ} × H_{σ} → A such that (F (T f))_{σ}(ξ, η) = Θ_{σ}X(F f)_{σ}(ξ, η) where F is the Fourier transform with the product × defined by : Θ_{σ}X(F f)_{σ}(ξ, η) = ∫_{G} Θ_{σ}(Ū_{σ}(t)ζ, η)dt, (ζ, η) ∈ H_{σ} × H_{σ}, U_{σ} ∈ σ. In this communication, and for further works, we extend the product × to all ordered pairs of sesquilinear mapping using their matrices (a_{tf}^{σ}), a_{tf}^{σ} = Θ_{σ}(ζ_{j}ζ_{i}) for an orthonormal basis of (ζ_{1}, …, ζ_{ησ}) of H_{σ}. Reference: V. S. K. Assiamoua, L_{1}(G, A) - multipliers, Acta Sci. Math. 53 (1989), 309-318. (*)