A remark on Toeplitz and Laurent operators acting on $\ell^p$ spaces with power weights

TY - JOUR

T1 - A remark on Toeplitz and Laurent operators acting on $\ell^p$ spaces with power weights

AU - Shargorodsky, Eugene

AU - Karlovych, Oleksiy

PY - 2024/6/19

Y1 - 2024/6/19

N2 - In the late 1980's, B\"ottcher and Silbermann asked whether the boundedness of the Toeplitz operator $T(a)$ on the space $\ell_\mu^p(\mathbb{Z}_+)$ implies boundedness of the Laurent operator $M(a)$ on the space $\ell_{0,\mu}^{p,p}(\mathbb{Z})$. We give the negative answer to this question.

AB - In the late 1980's, B\"ottcher and Silbermann asked whether the boundedness of the Toeplitz operator $T(a)$ on the space $\ell_\mu^p(\mathbb{Z}_+)$ implies boundedness of the Laurent operator $M(a)$ on the space $\ell_{0,\mu}^{p,p}(\mathbb{Z})$. We give the negative answer to this question.

M3 - Article

SN - 0024-3795

VL - 697

SP - 82

EP - 92

JO - LINEAR ALGEBRA AND ITS APPLICATIONS

JF - LINEAR ALGEBRA AND ITS APPLICATIONS

ER -