TY - CHAP

T1 - A survey on solvable sesquilinear forms

AU - Corso, Rosario

PY - 2018

Y1 - 2018

N2 - 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 reflexive 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.

AB - 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 reflexive 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.

UR - http://hdl.handle.net/10447/413747

M3 - Chapter

SN - 978-3-319-75995-1; 978-3-319-75996-8

T3 - OPERATOR THEORY

SP - 167

EP - 177

BT - The Diversity and Beauty of Applied Operator Theory

ER -