Abstract
It has been observed that the only Toeplitz operators that are isometric are those of the form To where q is an inner function on the unit disc (see e.g., [1, Theorem 8, Corollary 3]; the notation and terminology introduced there will be adhered to throughout this note). If we turn to the somewhat more general question of which Toeplitz operators are partial isometries, we see at once that the isometries TO, as well as their adjoints T,*,, are such, and a hasty inventory leads to the guess that there are no others. The purpose of this note is to prove that this is, in fact, the case.
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