Measurable schur multipliers and completely bounded multipliers of the Fourier algebras

Measurable Schur Multipliers and Completely Bounded Multipliers of the Fourier Algebras

Abstract. Let G be a locally compact group, L(G) be the usual Lspace for 1 ≤ p ≤ ∞ and A(G) be the Fourier algebra ofG. Our goal is to study, in a new abstract context, the completely bounded multipliers of A(G), which we denote McbA(G). We show that McbA(G) can be characterised as the “invariant part” of the space of (completely) bounded normal L∞(G)-bimodule maps on B(L(G)), the space of boun...

Multipliers of Multidimensional Fourier Algebras

Let G be a locally compact σ-compact group. Motivated by an earlier notion for discrete groups due to Effros and Ruan, we introduce the multidimensional Fourier algebra A(G) of G. We characterise the completely bounded multidimensional multipliers associated with A(G) in several equivalent ways. In particular, we establish a completely isometric embedding of the space of all n-dimensional compl...

FUNCTIONS ON MULTIPLIERS OF p-FOURIER ALGEBRAS

Transfer of Fourier multipliers into Schur multipliers and sumsets in a discrete group

We inspect the relationship between relative Fourier multipliers on noncommutative Lebesgue-Orlicz spaces of a discrete group Γ and relative Toeplitz-Schur multipliers on Schatten-von-Neumann-Orlicz classes. Four applications are given: lacunary sets, unconditional Schauder bases for the subspace of a Lebesgue space determined by a given spectrum Λ ⊆ Γ , the norm of the Hilbert transform and th...

Norms of idempotent Schur multipliers

Let D be a masa in B(H) where H is a separable Hilbert space. We find real numbers η0 < η1 < η2 < · · · < η6 so that for every bounded, normal D-bimodule map Φ on B(H), either ‖Φ‖ > η6 or ‖Φ‖ = ηk for some k ∈ {0, 1, 2, 3, 4, 5, 6}. When D is totally atomic, these maps are the idempotent Schur multipliers and we characterise those with norm ηk for 0 ≤ k ≤ 6. We also show that the Schur idempote...