On the decomposition theorem for meromorphic Fredholm resolvents

In this note results of B. Gramsch and W. Kaballo [8] on the decomposition of meromorphic (semi-) Fredholm resolvents are sharpened. A condition on an Orlicz function is given, under which the singular part in this decomposition can be chosen meromorphic inN, the ideal of -nuclear operators. Then the necessity of this condition is studied. Moreover, it is shown that for the rather steep Orlicz functions relevant to this question,N equalsS, the ideal of -approximable operators.Dedicated to Professor Albert Schneider on the occasion of his 60^th birthdayresearch supported by a grant from DAAD