Generalized slant Toeplitz operators on H 2

For an integer k ≥ 2, k th ‐order slant Toeplitz operator U φ [1] with symbol φ in L ∞ (), where is the unit circle in the complex plane, is an operator whose representing matrix M = ( α ij ) is given by α ij = 〈 φ , z ki–j 〉, where 〈. , .〉 is the usual inner product in L 2 (). The operator V φ denotes the compression of U φ to H 2 () (Hardy space). Algebraic and spectral properties of the operator V φ are discussed. It is proved that spectral radius of V φ equals the spectral radius of U φ , if φ is analytic or co‐analytic, and if T φ is invertible then the spectrum of V φ contains a closed disc and the interior of the disc consists of eigenvalues of infinite multiplicities. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)