6533b81ffe1ef96bd12770c9

RESEARCH PRODUCT

A survey on solvable sesquilinear forms

subject

description

The aim of this paper is to present a unified theory of many Kato type representation theorems in terms of solvable forms on a Hilbert space \((H,\langle\cdot,\cdot\rangle)\) In particular, for some sesquilinear forms Ω on a dense domain \(D\subseteq\mathcal {H}\) one looks for a representation \(\Omega(\xi,\eta)= \langle T\xi,\eta\rangle\) \((\xi\epsilon\mathcal{D}\mathcal(T),\eta\epsilon D)\) where T is a densely defined closed operator with domain \(D(\mathcal{T})\subseteq \mathcal{D}\). There are two characteristic aspects of a solvable form on H. One is that the domain of the form can be turned into a reexive Banach space that need not be a Hilbert space. The second one is that representation theorems hold after perturbing the form by a bounded form that is not necessarily a multiple of the inner product of H.