A characterization of idempotent Schur multipliers

2026/07/15 by Marcel K. Goh, Csongor Beke, Hamed Hatami +2
#math.CA #cs.CC #math.CO

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Abstract

We prove that every idempotent Schur multiplier is a finite signed sum of contractive idempotent Schur multipliers. This was conjectured by Katavolos and Paulsen in 2003 and previously known only for translation-invariant Schur multipliers, by the Cohen-Host idempotent theorem. Concretely, we show that any boolean matrix A with Schur multiplier norm at most~γ (or equivalently ‖ A‖_γ2 ≤ γ) can be written as A=∑_i=1^Lσ_i B_i, where L≤ 2^Cγ6 for an absolute constant C, σ_i∈\-1,1\ are signs, and each B_i is a contractive idempotent Schur multiplier, that is, a boolean matrix whose 1-entries form a union of all-one rectangular blocks, with no two blocks sharing a row or a column.

Citations

• On the Ranges of Bimodule Projections
• On a Conjecture of Littlewood and Idempotent Measures

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