  The issue of so-called maximal regularity is discussed within a Hilbert space
framework for a class of evolutionary equations. Viewing evolutionary equations
as a sums of two unbounded operators, showing maximal regularity amounts to
establishing that the operator sum considered with its natural domain is
already closed. For this we use structural constraints of the coefficients
rather than semi-group strategies or sesqui-linear form methods, which would be
difficult to come by for our general problem class. Our approach, although
limited to the Hilbert space case, complements known strategies for approaching
maximal regularity and extends them in a different direction. The abstract
findings are illustrated by re-considering some known maximal regularity
results within the framework presented.
