PUBLICATIONS DE L'INSTITUT MATHÉMATIQUE (BEOGRAD) (N.S.) Vol. 70(84), pp. 3741 (2001) 

SPECTRAL RADIUS AND SPECTRUM OF THE COMPRESSION OF A SLANT TOEPLITZ OPERATOR}Taddesse Zegeye and S.C. AroraDepartment of Mathematics, Bahir Dar University P.O Box 79, Bahir Dar, Ethiopia and Department of Mathematics, University of Delhi, Delhi 110007, IndiaAbstract: A slant Toeplitz operator $A_\varphi$ with symbol $\varphi$ in $L^\infty(T)$, where $T$ is the unit circle on the complex plane, is an operator whose representing matrix $M=(a_{i j})$ is given by $a_{ij}=\<\varphi, z^{2ij}\>$, where $\<\cdot,\cdot\>$ is the usual inner product in $L^2(T)$. The operator $B_\varphi$ denotes the compression of $A_\varphi$ to $H^2(T)$(Hardy space). In this paper, we prove that the spectral radius of $B_\varphi$ is greater than the spectral radius of $A_\varphi$, and if $\varphi$ and $\varphi^{1}$ are in $H^\infty$, then the spectrum of $B_\varphi$ contains a closed disc and the interior of this disc consists of eigenvalues with infinite multiplicity. Keywords: Toeplitz operator; slant Toeplitz operator; compression; spectrum Classification (MSC2000): 47B35; 47A10 Full text of the article:
Electronic fulltext finalized on: 17 Oct 2002. This page was last modified: 13 Nov 2002.
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