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In this paper we completely characterize compact commutator of two Toeplitz operators on the Hardy space of the unit circle. and Condition 0.5 is equivalent to The following theorem is the version of our main result in terms of Douglas algebras. Theorem 0.6. The commutator [T f , T g ] of two Toeplitz operators is compact if and only ifdoi:10.2140/pjm.1999.190.87 fatcat:wlbu54jgq5ffho3qw3seleieda