Geodesic
Toeplitz operators with $C+H^\infty$ symbols on~$l^p$
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part XVI, Tome 157 (1987), pp. 124-128

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We show that the algebra of all multipliers on $l^p$ $(1$ contains a closed subalgebra, $C_p+H_p^\infty$, which coincides with the familiar algebra $C+H^\infty$ in the case $p=2$. We also prove that a Toeplitz operator with $C_p+H_p^\infty$ symbol is Fredholm on $l^p$ if and only if its symbol is invertible in $C_p+H_p^\infty$. 
@article{ZNSL_1987_157_a10,
     author = {A. B\"ottcher and B. Silbermann},
     title = {Toeplitz operators with $C+H^\infty$ symbols on~$l^p$},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {124--128},
     publisher = {mathdoc},
     volume = {157},
     year = {1987},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1987_157_a10/}
}
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A. Böttcher; B. Silbermann. Toeplitz operators with $C+H^\infty$ symbols on~$l^p$. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part XVI, Tome 157 (1987), pp. 124-128. http://geodesic.mathdoc.fr/item/ZNSL_1987_157_a10/