# Bounded and compact Toeplitz+Hankel matrices

Ehrhardt, T., Hagger, R. and Virtanen, J. (2021) Bounded and compact Toeplitz+Hankel matrices. Studia Mathematica. ISSN 0039-3223

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To link to this item DOI: 10.4064/sm200806-6-10

## Abstract/Summary

We show that an infinite Toeplitz+Hankel matrix $T(\varphi) + H(\psi)$ generates a bounded (compact) operator on $\ell^p(\mathbb{N}_0)$ with $1\leq p\leq \infty$ if and only if both $T(\varphi)$ and $H(\psi)$ are bounded (compact). We also give analogous characterizations for Toeplitz+Hankel operators acting on the reflexive Hardy spaces. In both cases, we provide an intrinsic characterization of bounded operators of Toeplitz+Hankel form similar to the Brown-Halmos theorem. In addition, we establish estimates for the norm and the essential norm of such operators.

Item Type: Article Yes Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics 93267 Institute of Mathematics Polish Academy of Sciences