6533b858fe1ef96bd12b6d19
RESEARCH PRODUCT
Representation Theorems for Solvable Sesquilinear Forms
Rosario CorsoCamillo Trapanisubject
Pure mathematics47A07 47A30Banach spaceStructure (category theory)01 natural sciencesBanach-Gelfand tripletCompatible normOperator (computer programming)Kato's first representation theoremFOS: Mathematics0101 mathematicsRepresentation (mathematics)Numerical rangeMathematics::Representation TheoryMathematicsMathematics::Functional AnalysisAlgebra and Number TheorySesquilinear formMathematics::Operator Algebras010102 general mathematicsFunctional Analysis (math.FA)Mathematics - Functional Analysis010101 applied mathematicsq-closed and solvable sesquilinear formDomain (ring theory)IsomorphismAnalysisdescription
New results are added to the paper [4] about q-closed and solvable sesquilinear forms. The structure of the Banach space $\mathcal{D}[||\cdot||_\Omega]$ defined on the domain $\mathcal{D}$ of a q-closed sesquilinear form $\Omega$ 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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2017-02-02 |