On the Arazy conjecture concerning Schur multipliers on Schatten ideals

We confirm in the affirmative the conjecture made by Arazy in [2]. Suppose that f is a continuously differentiable function on [−1,1] such that|f′(t)|≤C|t|α,t∈[−1,1], for some constant C>0 and 0<α<∞. Let {λj}j=1∞∈ℓr for some 0