Some remarks on Toeplitz multipliers and Hankel matrices

Aleksander Pełczyński, and Fyodor Sukochev. "Some remarks on Toeplitz multipliers and Hankel matrices." Studia Mathematica 175.2 (2006): 175-204. <http://eudml.org/doc/286309>.

@article{AleksanderPełczyński2006,
abstract = {Consider the set of all Toeplitz-Schur multipliers sending every upper triangular matrix from the trace class into a matrix with absolutely summable entries. We show that this set admits a description completely analogous to that of the set of all Fourier multipliers from H₁ into ℓ₁. We characterize the set of all Schur multipliers sending matrices representing bounded operators on ℓ₂ into matrices with absolutely summable entries. Next, we present a result (due to G. Pisier) that the upper triangular parts of such Schur multipliers are precisely the Schur multipliers sending upper triangular parts of matrices representing bounded linear operators on ℓ₂ into matrices with absolutely summable entries. Finally, we complement solutions of Mazur's Problems 8 and 88 in the Scottish Book concerning Hankel matrices.},
author = {Aleksander Pełczyński, Fyodor Sukochev},
journal = {Studia Mathematica},
keywords = {upper triangular matrix; Toeplitz matrix; Hankel matrix; Schur product; Schur multiplier; Fourier multiplier},
language = {eng},
number = {2},
pages = {175-204},
title = {Some remarks on Toeplitz multipliers and Hankel matrices},
url = {http://eudml.org/doc/286309},
volume = {175},
year = {2006},
}

TY - JOUR
AU - Aleksander Pełczyński
AU - Fyodor Sukochev
TI - Some remarks on Toeplitz multipliers and Hankel matrices
JO - Studia Mathematica
PY - 2006
VL - 175
IS - 2
SP - 175
EP - 204
AB - Consider the set of all Toeplitz-Schur multipliers sending every upper triangular matrix from the trace class into a matrix with absolutely summable entries. We show that this set admits a description completely analogous to that of the set of all Fourier multipliers from H₁ into ℓ₁. We characterize the set of all Schur multipliers sending matrices representing bounded operators on ℓ₂ into matrices with absolutely summable entries. Next, we present a result (due to G. Pisier) that the upper triangular parts of such Schur multipliers are precisely the Schur multipliers sending upper triangular parts of matrices representing bounded linear operators on ℓ₂ into matrices with absolutely summable entries. Finally, we complement solutions of Mazur's Problems 8 and 88 in the Scottish Book concerning Hankel matrices.
LA - eng
KW - upper triangular matrix; Toeplitz matrix; Hankel matrix; Schur product; Schur multiplier; Fourier multiplier
UR - http://eudml.org/doc/286309
ER -