For φ in L^∞ (∂ D), let φ = f + g where f and g are in H². In this note, it is shown that the Toeplitz operator Tφ is hyponormal if and only if g = c + Tₕf for some constant c and some function h in H^∞ (D) with \| h \|_∞ ≤ 1.
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Carl C. Cowen (1988) studied this question.