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- W2022382038 abstract "In this paper we discuss the asymptotic distribution of the approximation numbers of the finite sections for a Toeplitz operator T ( a ) ∈ L ( ℓ p ) , 1 < p < ∞ , where a is a piecewise continuous function on the unit circle. We prove that the behavior of the approximation numbers of the finite sections T n ( a ) = P n T ( a ) P n depends heavily on the Fredholm properties of the operators T ( a ) and T ( a ˜ ) ( a ˜ ( t ) = a ( 1 / t ) ) . In particular, if the operators T ( a ) and T ( a ˜ ) are Fredholm on ℓ p , then the approximation numbers of T n ( a ) have the so-called k -splitting property. But, in contrast with the case of continuous symbols, the splitting number k is in general larger than dim ker T ( a ) + dim ker T ( a ˜ ) ." @default.
- W2022382038 created "2016-06-24" @default.
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- W2022382038 date "2006-08-01" @default.
- W2022382038 modified "2023-09-26" @default.
- W2022382038 title "Approximation numbers for the finite sections of Toeplitz operators with piecewise continuous symbols" @default.
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- W2022382038 doi "https://doi.org/10.1016/j.jfa.2006.02.004" @default.
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