Basic representation theorems of forms

2025/05/14 by Zoltán Sebestyén, Sebestyén, Zoltán, Zsigmond Tarcsay +1
Engineering · #47A07 #47A20 #Advanced Numerical Analysis Techniques #FOS: Mathematics #Functional Analysis (math.FA)

paper · pdf · doi:10.48550/arxiv.2505.09588

openalex publication_date 2025/05/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study maximal representations of nonnegative sesquilinear forms in real or complex Hilbert spaces, that are not necessarily closed or even closable. We associate positive self-adjoint operators with such forms, in a sense similar to Kato's representation theorems. In particular, we give a brief proof of the Friedrichs extension of a densely defined positive operator.

Citations

• On the adjoint of Hilbert space operators

Related

• Some Representation Theorems for Sesquilinear Forms
• Various form closures associated with a fixed non-semibounded self-adjoint operator
• A Short-type Decomposition Of Forms
• Representing maps for semibounded forms and their Lebesgue type decompositions
• Positive Definite Operator Functions and Sesquilinear Forms