• DOI:10.1112/S0024611504014650
• Corpus ID: 310844

Measurable Schur Multipliers and Completely Bounded Multipliers of the Fourier Algebras

@article{Spronk2002MeasurableSM,
  title={Measurable Schur Multipliers and Completely Bounded Multipliers of the Fourier Algebras},
  author={Nico Spronk},
  journal={Proceedings of the London Mathematical Society},
  year={2002},
  volume={89}
}

• N. Spronk
• Published 19 October 2002
• Mathematics
• Proceedings of the London Mathematical Society

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).