English

On semibounded Toeplitz operators

Functional Analysis 2016-05-25 v2 Classical Analysis and ODEs Spectral Theory

Abstract

We show that a semibounded Toeplitz quadratic form is closable in the space 2(Z+)\ell^2({\Bbb Z}_{+}) if and only if its matrix elemens are Fourier coefficients of an absolutely continuous measure. We also describe the domain of the corresponding closed form. This allows us to define semibounded Toeplitz operators under minimal assumptions on their matrix elements.

Keywords

Cite

@article{arxiv.1603.06229,
  title  = {On semibounded Toeplitz operators},
  author = {D. R. Yafaev},
  journal= {arXiv preprint arXiv:1603.06229},
  year   = {2016}
}

Comments

This is a slightly revised version of the article, arXiv:1603.06229v1, with the same tittle. Some misprints has been removed and some arguments has been made more clear. The results are unchaged. To appear in J. Operator theory

R2 v1 2026-06-22T13:14:46.526Z