Basic representation theorems of forms (2505.09588v1)

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.