Journal of the
Korean Mathematical Society
JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

Article

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J. Korean Math. Soc. 2019; 56(3): 703-721

Online first article February 12, 2019      Printed May 1, 2019

https://doi.org/10.4134/JKMS.j180324

Copyright © The Korean Mathematical Society.

Slant H-Toeplitz operators on the Hardy space

Anuradha Gupta, Shivam Kumar Singh

University of Delhi; University of Delhi

Abstract

The notion of slant H-Toeplitz operator $V_\phi$ on the Hardy space $H^2$ is introduced and its characterizations are obtained. It has been shown that an operator on the space $H^2$ is a slant H-Toeplitz if and only if its matrix is a slant H-Toeplitz matrix. In addition, the conditions under which slant Toeplitz and slant Hankel operators become slant H-Toeplitz operators are also obtained.

Keywords: Toeplitz operator, Hankel operator, slant Toeplitz operator, slant Hankel operator, H-Toeplitz operator

MSC numbers: Primary 47B35; Secondary 47B32

Supported by: Support of CSIR Research Grant to second author [F.No. 09/045(1405)/2015-EMR-I] for carrying out the research work is fully
acknowledged.