  The aim of this paper is to present a unified theory of many Kato type
representation theorems in terms of solvable forms on Hilbert spaces. In
particular, for some sesquilinear forms $\Omega$ on a dense domain
$\mathcal{D}$ one looks for an expression $$
  \Omega(\xi,\eta)=\langle T\xi , \eta\rangle, \qquad \forall \xi\in D(T),\eta
\in \mathcal{D},
  $$ where $T$ is a densely defined closed operator with domain $D(T)\subseteq
\mathcal{D}$. There are two characteristic aspects of solvable forms. Namely,
one is that the domain of the form can be turned into a reflexive Banach space
need not be a Hilbert space. The second one is the existence of a perturbation
with a bounded form which is not necessarily a multiple of the inner product.
