Geodesic
Spectral Radius and Spectrum of the Compression of a Slant Toeplitz Operator}
Publications de l'Institut Mathématique, _N_S_70 (2001) no. 84, p. 37 Cet article a éte moissonné depuis la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

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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 $a_{ij}=\\varphi, z^{2i-j}\>$, 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.
Classification : 47B35 47A10
Keywords: Toeplitz operator, slant Toeplitz operator, compression, spectrum 
@article{PIM_2001_N_S_70_84_a4,
     author = {Taddesse Zegeye and S.C. Arora},
     title = {Spectral {Radius} and {Spectrum} of the {Compression} of a {Slant} {Toeplitz} {Operator}}},
     journal = {Publications de l'Institut Math\'ematique},
     pages = {37 },
     year = {2001},
     volume = {_N_S_70},
     number = {84},
     zbl = {1029.47015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PIM_2001_N_S_70_84_a4/}
}
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Taddesse Zegeye; S.C. Arora. Spectral Radius and Spectrum of the Compression of a Slant Toeplitz Operator}. Publications de l'Institut Mathématique, _N_S_70 (2001) no. 84, p. 37 . http://geodesic.mathdoc.fr/item/PIM_2001_N_S_70_84_a4/