Accessibility navigation

Bounded and compact Toeplitz+Hankel matrices

Ehrhardt, T., Hagger, R. and Virtanen, J. (2020) Bounded and compact Toeplitz+Hankel matrices. Studia Mathematica. ISSN 0039-3223 (In Press)

[img] Text - Accepted Version
· Restricted to Repository staff only
· The Copyright of this document has not been checked yet. This may affect its availability.


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


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
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

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

Page navigation