Let rm, n=Pm, n/ Qm, n be the Padé approximation of order (m, n) for a given power series f: Qm, nf- Pm, n= O(zm+n+1+j), j is as large as possible, m′ ,n′ are the exact degree of pm, n and Qm, n respectively and d = min{m-m′ ,n-n′}. Let Tm, n be the operator that maps f on rm, n . Then Tm, n is continuous if and only if d + (j-|j|)/2= 0. This condition is equal to that rm, n is on the border of a Padé block.The results obtained by H. Werner and L.Wuytack have been modified and cor reeled in this paper. |