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Some remarks on Toeplitz multipliers and Hankel matrices

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Pełczyński A., Sukochev F.

Studia Mathematica

2006

tom 175

nr 2

175-204

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.

Ograniczanie wyników

1 Studia Mathematica

1 Pełczyński A.

1 Sukochev F.

1 2006

Wyniki wyszukiwania

Some remarks on Toeplitz multipliers and Hankel matrices