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Let B be an accretive operator on a complex Hilbert space and let V be the classical Volterra operator on L 2 (0, 1). We study a contraction property for (I −mB)(I +B) −1 , m ∈ ℝ. In particular, we show that ‖(I −mV)(I+V) −1 ‖ = 1 only for m ∈ [−1, 1].

Some Norm one Functions of the Volterra Operator