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We study idempotent, model, and Toeplitz operators that attain the norm. Notably, we prove that if 𝒬 is a backward shift invariant subspace of the Hardy space H^2(𝔻), then the model operator S_𝒬 attains its norm. Here S_𝒬 = P_𝒬M_z|_𝒬, the compression of the shift M_z on the Hardy space H^2(𝔻) to 𝒬.arXiv:2101.03585v2 fatcat:qajo2tfrizhw3krulbrwecpwty