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,⟨‹…,‹…⟩) In particular, for some sesquilinear forms Ω on a dense domain D ⊆ H one looks for a representation Ω(ξ, η) = ⟨Tξ, η⟩ (ξ ϵ D(T), η ϵ D where T is a densely defined closed operator with domain D(T) ⊆ 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.
CITATION STYLE
Corso, R. (2018). A survey on solvable sesquilinear forms. In Operator Theory: Advances and Applications (Vol. 268, pp. 167–177). Springer International Publishing. https://doi.org/10.1007/978-3-319-75996-8_9
Mendeley helps you to discover research relevant for your work.