The study finds an association between sesquilinear forms and positive self-adjoint operators, suggesting insights into Kato's representation theorems.
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.
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Sebestyén et al. (2025) studied this question.
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