Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part XVI, Tome 157 (1987), pp. 124-128
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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/
@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},
year = {1987},
volume = {157},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_1987_157_a10/}
}
TY - JOUR
AU - A. Böttcher
AU - B. Silbermann
TI - Toeplitz operators with $C+H^\infty$ symbols on $l^p$
JO - Zapiski Nauchnykh Seminarov POMI
PY - 1987
SP - 124
EP - 128
VL - 157
UR - http://geodesic.mathdoc.fr/item/ZNSL_1987_157_a10/
LA - ru
ID - ZNSL_1987_157_a10
ER -
%0 Journal Article
%A A. Böttcher
%A B. Silbermann
%T Toeplitz operators with $C+H^\infty$ symbols on $l^p$
%J Zapiski Nauchnykh Seminarov POMI
%D 1987
%P 124-128
%V 157
%U http://geodesic.mathdoc.fr/item/ZNSL_1987_157_a10/
%G ru
%F ZNSL_1987_157_a10
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 $C_p+H_p^\infty$.
