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.

Corso R. (2018). A survey on solvable sesquilinear forms. In A. Böttcher, D. Potts, P. Stollmann, D. Wenzel (a cura di), The Diversity and Beauty of Applied Operator Theory (pp. 167-177). Springer International Publishing [10.1007/978-3-319-75996-8_9].

A survey on solvable sesquilinear forms

Corso R.
2018-01-01

Abstract

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.
2018
Settore MAT/05 - Analisi Matematica
Corso R. (2018). A survey on solvable sesquilinear forms. In A. Böttcher, D. Potts, P. Stollmann, D. Wenzel (a cura di), The Diversity and Beauty of Applied Operator Theory (pp. 167-177). Springer International Publishing [10.1007/978-3-319-75996-8_9].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10447/413747
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