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Bulletin of the London Mathematical Society (1)

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ON THE APPROXIMATION NUMBERS FOR THE FINITE SECTIONS OF BLOCK TOEPLITZ MATRICES
A. ROGOZHIN, B. SILBERMANN
Journal:

Bulletin of the London Mathematical Society / Volume 38 / Issue 2 / April 2006

Published online by Cambridge University Press:

16 March 2006, pp. 301-313

Print publication:

April 2006
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In this paper we discuss the asymptotic distribution of the approximation numbers of the finite sections for a Toeplitz operator $T(a) \in \mathcal{L}(\ell^{p,\mu}_N)$, $1 < p < \infty$ and $\mu \in \mathbb{R}$, with a continuous matrix-valued generating function $a$. We prove that the approximation numbers of the finite sections $T_n(a) = P_n T(a) P_n$ have the $k$-splitting property, provided $T(a)$ is a Fredholm operator on $\ell^{p,\mu}_N$.