arXiv subjects

Rosario Corso

Publications and source records attributed to Rosario Corso.

20 records · Page 2Linked to original sources

arXiv2017

A Survey on Solvable Sesquilinear Forms

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 $Ω$ on a dense domain $\mathcal{D}$ one looks for an expression $$ Ω(ξ,η)=\langle Tξ, η\rangle, \qquad \forall ξ\in D(T),η\in \mathcal{D}, $$ 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.

math.FA↗

arXiv2017

Representation Theorems for Solvable Sesquilinear Forms

New results are added to the paper [4] about q-closed and solvable sesquilinear forms. The structure of the Banach space $\mathcal{D}[||\cdot||_Ω]$ defined on the domain $\mathcal{D}$ of a q-closed sesquilinear form $Ω$ is unique up to isomorphism, and the adjoint of a sesquilinear form has the same property of q-closure or of solvability. The operator associated to a solvable sesquilinear form is the greatest which represents the form and it is self-adjoint if, and only if, the form is symmetric. We give more criteria of solvability for q-closed sesquilinear forms. Some of these criteria are related to the numerical range, and we analyse in particular the forms which are solvable with respect to inner products. The theory of solvable sesquilinear forms generalises those of many known sesquilinear forms in literature.

math.FA↗