New results are added to the paper (Di Bella and Trapani in J Math Anal Appl 451:64-83, 2017) about q-closed and solvable sesquilinear forms. The structure of the Banach space defined on the domain of a q-closed sesquilinear form 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.

Corso, R., Trapani, C. (2017). Representation Theorems for Solvable Sesquilinear Forms. INTEGRAL EQUATIONS AND OPERATOR THEORY, 89(1), 43-68 [10.1007/s00020-017-2387-5].

### Representation Theorems for Solvable Sesquilinear Forms

#### Abstract

New results are added to the paper (Di Bella and Trapani in J Math Anal Appl 451:64-83, 2017) about q-closed and solvable sesquilinear forms. The structure of the Banach space defined on the domain of a q-closed sesquilinear form 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.
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2017
Corso, R., Trapani, C. (2017). Representation Theorems for Solvable Sesquilinear Forms. INTEGRAL EQUATIONS AND OPERATOR THEORY, 89(1), 43-68 [10.1007/s00020-017-2387-5].
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/10447/244277`