TY - JOUR

T1 - Representation Theorems for Solvable Sesquilinear Forms

AU - Corso, Rosario

AU - Trapani, Camillo

PY - 2017

Y1 - 2017

N2 - 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.

AB - 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.

KW - Banach-Gelfand triplet

KW - Compatible norms

KW - Kato's first representation theorem

KW - q-closed and solvable sesquilinear forms

KW - Banach-Gelfand triplet

KW - Compatible norms

KW - Kato's first representation theorem

KW - q-closed and solvable sesquilinear forms

UR - http://hdl.handle.net/10447/244277

M3 - Article

VL - 89

SP - 43

EP - 68

JO - Integral Equations and Operator Theory

JF - Integral Equations and Operator Theory

SN - 0378-620X

ER -