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On the Approximation Numbers for the Finite Sections of Block Toeplitz Matrices

Authors:	Rogozhin A; Silbermann B

Institution:	Department of Mathematics, Chemnitz University of Technology D09107 Chemnitz, Germany Alexander.Rogozhin{at}mathematik.tu-chemnitz.de, bernd.silbermann{at}mathematik.tu-chemnitz.de

Abstract:	In this paper we discuss the asymptotic distribution of theapproximation numbers of the finite sections for a Toeplitzoperator and µ $isin$ R, witha continuous matrix-valued generating function a. We prove thatthe approximation numbers of the finite sections T_n(a) = P_nT(a)P_nhave the k-splitting property, provided T(a) is a Fredholm operatoron . 2000 Mathematics SubjectClassification 47B35 (primary), 15A18, 47A58, 47A75, 65F20 (secondary).

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