Measurable Schur Multipliers and Completely Bounded Multipliers of the Fourier Algebras
By N. Spronk. 2002
105 citations recorded by the source corpus.
Let G be a locally compact group, Lp(G) be the usual Lp‐space for 1 ⩽ p ⩽ ∞, and A(G) be the Fourier algebra of G. 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(L2(G)), the space of bounded operators on L2(G). In doing this we develop a function‐theoretic description of the normal L∞(X, μ)‐bimodule maps on B(L2(X, μ)), which we denote by V∞(X, μ), and name the measurable Schur multipliers of (X, μ). Our approach leads to many new results, some of which generalise results hitherto known only for certain classes of groups. Those results which we develop here are a uniform approach to obtaining the functorial properties of McbA(G), and a concrete description of a standard predual of McbA(G). 2000 Mathematics Subject Classification 46L07, 43A30, 43A15, 46A32, 22D10, 22D12 (primary), 22D25, 43A20, 43A07 (secondary).
Subfields: Algebra and Number Theory, Applied Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/bb5b6b4fee331b941844ca9fd4f930ffd040d573
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Algebra and Number Theory
In Applied Mathematics
In Mathematical Physics
Citations in the corpus
- Multipliers, Self-Induced and Dual Banach Algebras (2010, background): “There has been considerable interest in multipliers as applied to abstract (quantum) harmonic analysis, see [20, 26, 22, 52, 40] for example.”