2025/05/30 by Christensen, Erik
#15A39 #15A45 #15A60 #46L07 #47A30 #81P47 #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA)
paper · doi:10.48550/arxiv.2505.24670
We present a formula for the Schur multiplier norm of a complex self-adjoint matrix, and a formula for the norm, which is dual to the Schur multiplier norm, of a self-adjoint matrix. For a complex self-adjoint n × n matrix X we show that its Schur multiplier norm is determined by ‖X‖S = min \ ‖diag(P)‖_∞ : - P ≤ X ≤ P \. The dual space of ( Mn(\bc), ‖.‖S) is (Mn(\bc), ‖.‖cbB). For X=X^*: ‖X‖cbB = min \ Trn(Δ(λ)) : λ∈ \brn, - Δ(λ) ≤ X ≤ Δ(λ) \.