Abstract
The spectral theory of operators in Banach spaces is employed to treat a class of degenerate evolution equations. A basic role is played by the assumption that the Banach space under consideration may be expressed as a direct sum of two suitable subspaces. Two methods for solving the problem are studied. The first method is based on the expansion of the resolvent of a closed operator into Laurent series in a neighbourhood of 0. The second one makes use of the theory of abstract potential operators. In particular, an extension of the Hille-Yosida theorem on infinitesimal generators of ( C 0) semigroups of linear operators is obtained. Some examples relative to operators appearing in many applications to partial differential equations are given.
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