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A sufficient condition is given for the compactness of the evolution operator      U ( t , s ) U(t,s)       generated by a family of nonlinear      ω  \omega      -accretive operators      A ( t ) A(t)      . This family      A ( t ) A(t)       satisfies a time-dependence condition which is not covered by the results of Calvert and the author. It is also shown that the main part of this sufficient condition is necessary.

On the compactness of the evolution operator generated by certain nonlinear Ω-accretive operators in general Banach spaces