# A canonical decomposition for quadratic forms with applications to monotone convergence theorems

@article{Simon1978ACD, title={A canonical decomposition for quadratic forms with applications to monotone convergence theorems}, author={B. Simon}, journal={Journal of Functional Analysis}, year={1978}, volume={28}, pages={377-385} }

We prove monotone convergence theorems for quadratic forms on a Hilbert space which improve existing results. The main tool is a canonical decomposition for any positive quadratic form h = hr + hs where hr is characterized as the largest closable form smaller than h. There is also a systematic discussion of nondensely defined forms.

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