Basic Representation Theorems of Forms

Tarcsay, Zsigmond ORCID: https://orcid.org/0000-0001-8102-5055 and Sebestyén, Zoltán ORCID: https://orcid.org/0000-0002-2382-8797 (2025) Basic Representation Theorems of Forms. Complex Analysis and Operator Theory, 19 (7). DOI 10.1007/s11785-025-01806-3

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Official URL: https://doi.org/10.1007/s11785-025-01806-3

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.

Item Type:

Article

Uncontrolled Keywords:

Friedrichs extension; self-adjoint operator; Nonnegative form; Representation of forms;

JEL classification:

C02 - Mathematical Methods

Divisions:

Institute of Data Analytics and Information Systems

Subjects:

Mathematics, Econometrics

Funders:

Corvinus University of Budapest, Hungarian Scientific Research Fund, National Research, Development and Innovation Fund