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For α ∈ [0, 1] the operator 
is the operator formally defined on the Hardy space H2 by
If α = 1, then the usual identification of H2 with l2 takes A 1 onto the discrete Cesàro operator. Here we see that {A α : α ∈ [0, 1]} is not arcwise connected, that Re A α ≥ 0, that A α is a Hilbert-Schmidt operator if α ∈[0, 1), and that A α is neither normaloid nor spectraloid if α ∈(0, 1).
