PUBLICATIONS DE L'INSTITUT MATHEMATIQUE (BEOGRAD) (N.S.) Vol. 74(88), pp. 129–136 (2003) 

THE COMPRESSION OF A SLANT HANKEL OPERATOR TO $H^2$Taddesse Zegeye and S. C. AroraBahir Dar University, Department of Mathematics, Bahir Dar, Ethiopia and Department of Mathematics, University of Delhi, IndiaAbstract: A slant Hankel operator $K_{\varphi}$ with symbol $\varphi$ in $L^{\infty}(T)$ (in short $L^{\infty})$, where $T$ is the unit circle on the complex plane, is an operator whose representing matrix $M=(a_{ij})$ is given by $a_{i,j}=<\varphi,z^{2ij}\>$, where $<\cdot,\cdot\>$ is the usual inner product in $L^2(T)$ (in short $L^2)$. The operator $L_{\varphi}$ denotes the compression of $K_{\varphi}$ to $H^2(T)$ (in short $H^2$). We prove that an operator $L$ on $H^2$ is the compression of a slant Hankel operator to $H^2$ if and only if $U*L=LU^2$, where $U$ is the unilateral shift. Moreover, we show that a hyponormal $L_{\varphi}$ is necessarily normal and $L_{\varphi}$ can not be an isometry. Keywords: Toeplitz poerator, slant Toeplitz operator, Hankel operator, slant Hankel operator Classification (MSC2000): 47D99 Full text of the article: (for faster download, first choose a mirror)
Electronic fulltext finalized on: 21 Dec 2004. This page was last modified: 9 Feb 2005.
© 2004 Mathematical Institute of the Serbian Academy of Science and Arts
