A Baxter operator is a linear operator T on a Banach algebra 2I which satisfies the identity Tx.Ty=T(Tx.y+x.Ty-thy) for all x and y in VI, 0 being some fixed element of %. The consequences of this identity were first explored by G. Baxter [l], and subsequently by J. G. Wendel [2], J. F. C. Kingman [3], [4], F. V. Atkinson [S] and the author [6]. The two last-mentioned papers give a partial description of the spectral properties of bounded Baxter operators. While [6] provides a fairly explicit formula for the resolvent R(X, T) = (XI T)-l of T, this formula contains the resolvent of 0, in a way which seems to make the resolvent set Res( T) of T depend upon that of 8; at any rate, the extent of Res( T) in the general case is in doubt, and for the proof of the formula in [6] it was assumed that h belongs to the unbounded component of [Res( 2’) n Res(ffll\(O>. In the present paper we consider only the case 0 = e, where e is the identity element in 91. This case is still of much interest, and has already been studied in some detail. In [6] it was shown that T has a certain summation property when restricted to functions of the element t = Te, which can be written heuristically as