Böttcher, A.; Silbermann, B. Toeplitz operators with symbols from \(C+H^{\infty}\) in the spaces \(\ell\) p. (Russian. English summary) Zbl 0643.47029 Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova 157, 124-128 (1987). The authors describe a closed subalgebra \(C_ p+H_ p^{\infty}\) of all multipliers on \(\ell\) p \((1<p<\infty)\) with the following property: A Toeplitz operator with symbol in \(C_ p+H_ p^{\infty}\) is a Fredholm operator in \(\ell\) p if and only if its symbol is invertible in \(C_ p+H_ p^{\infty}\). \(C_ 2+H_ 2^{\infty}=C+H^{\infty}\) holds. Reviewer: K.-H.Förster Cited in 1 ReviewCited in 1 Document MSC: 47B35 Toeplitz operators, Hankel operators, Wiener-Hopf operators 47A53 (Semi-) Fredholm operators; index theories Keywords:closed subalgebra of multipliers; Fredholm operator PDFBibTeX XMLCite \textit{A. Böttcher} and \textit{B. Silbermann}, Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova 157, 124--128 (1987; Zbl 0643.47029)