Recently J. B. Reade determined the spectrum of C, the Cesaro matrix of order 1, considered as an operator on c 0 , the space of null sequences. Previously F. P. A. Cass and the author had determined the spectra for a large class of weighted mean operators on c, the space of convergent sequences. Subsequently the author determined the fine spectra of these operators over c. This paper examines the spectra and fine spectra of weighted mean operators on c 0 , obtaining the result of Reade as a

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... cial case. In a recent paper Reade [4] determined the spectrum of C, the Cesaro matrix of order 1, regarded as a member of B(c 0 ); i.e. a bounded linear operator on the space c 0 of null sequences. In 1977 Cass and the author [1] determined the spectra for a large class of weighted mean operators in B(c), c the space of convergent sequences. More recently the author [5] determined the fine spectra of these operators, again in B(c). This paper extends [1] and [5] to B(c 0 ), and obtains the result of [4] as a special case. A weighted mean matrix is a triangular matrix A = (a nk ) with a nk = /^/^, where p 0 > 0, p n ^ 0 for n > 0, and P n = 2£ =0 Pk-If P n ~* °° tnen A e B(c) and B(c 0 ). Let o(A) denote the spectrum of A in B(c 0 ).