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Assume that A generates a solution operator S α ( t ).
It is known that A generates an analytic semigroup in both H and V*.
In this paper, we suppose that A generates an equicontinuous semigroup T ( t ) on X.
It is known that A generates a compact semigroup S ( t ), t > 0, in X and is given by.
It is well known that A generates a strongly continuous semigroup { T ( t ) } t ≥ 0 which is compact, analytic, and self-adjoint.
It is well known that A generates an analytic (and hence immediately norm continuous) and compact (C_{0} -semigroup (T(t)) on X.
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CEO of Professional Science Editing for Scientists @ prosciediting.com