Contraction semigroups of
linear operators on a Banach space appear in a wide variety of physical and
mathematical situations, and for this reason there has been much interest attached to
studying the properties of such semigroups and their infinitesimal generators. In this
paper we examine in some detail the question of when one can (left or right)
multiply the infinitesimal generator A by another (bounded or unbounded)
operator B and still preserve the generator property. Also, we state when
polynomials in a generator retain the generator property. Our treatment is not
exhaustive but is meant to be representative of the type of results which may be
obtained.
