Accessibility navigation


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

[img]
Preview
Text - Accepted Version
· Please see our End User Agreement before downloading.

407kB

It is advisable to refer to the publisher's version if you intend to cite from this work. See Guidance on citing.

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
Refereed:Yes
Divisions:Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
ID Code:93267
Publisher:Institute of Mathematics Polish Academy of Sciences

Downloads

Downloads per month over past year

University Staff: Request a correction | Centaur Editors: Update this record

Page navigation