Products of truncated Hankel operators and truncated Toeplitz operators

Abstract

A truncated Hankel operator $B_f^{\theta }:K_{\theta }\to K_{\theta }$ is a compression of a Hankel operator $H_f:H^2\to H^2$ to a model space $K_{\theta }$. In this paper we firstly characterize when a bounded truncated Hankel operator is compact. Then we study the product of a truncated Hankel operator and a truncated Toeplitz operator, and prove, for some special symbols, several necessary and sufficient conditions for the product to be zero or compact respectively.

COMMUNICATED BY:

• J. Virtanen

Keywords:

• Truncated Hankel operator
• truncated Toeplitz operator
• model space
• maximal ideal space
• compact operator

AMS Subject Classifications:

• 47B35
• 47B32

Acknowledgments

We are grateful to the referees for his helpful suggestions which improved the presentation of the paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work is partially supported by the NSFC [grant number 11971087].