In this paper the notion of slant Hankel operator $K_\varphi$, with symbol $\varphi$ in $L^\infty$, on the space $L^2({\Bbb T})$, ${\Bbb T}$ being the unit circle, is introduced. The matrix of the slant Hankel operator with respect to the usual basis $\{z^i : i \in {\Bbb Z} \}$ of the space $L^2$ is given by $\langle\alpha_{ij}\rangle = \langle a_{-2i-j}\rangle$, where $\sum\limits_{i=-\infty}^{\infty}a_i z^i$ is the Fourier expansion of $\varphi$. Some algebraic properties such as the norm, compactness of the operator $K_\varphi$ are discussed. Along with the algebraic properties some spectral properties of such operators are discussed. Precisely, it is proved that for an invertible symbol $\varphi$, the spectrum of $K_\varphi$ contains a closed disc.
@article{107988,
author = {Subhash Chander Arora and Ruchika Batra and M. P. Singh},
title = {Slant Hankel operators},
journal = {Archivum Mathematicum},
volume = {042},
year = {2006},
pages = {125-133},
zbl = {1164.47325},
mrnumber = {2240189},
language = {en},
url = {http://dml.mathdoc.fr/item/107988}
}
Arora, Subhash Chander; Batra, Ruchika; Singh, M. P. Slant Hankel operators. Archivum Mathematicum, Tome 042 (2006) pp. 125-133. http://gdmltest.u-ga.fr/item/107988/
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