Some remarks on Toeplitz multipliers and Hankel matrices

• Autorzy: Aleksander Pełczyński , Fyodor Sukochev
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 47B49: Transformers, preservers (operators on spaces of operators)
• 15A60: Norms of matrices, numerical range, applications of functional analysis to matrix theory
• 47B35: Toeplitz operators, Hankel operators, Wiener-Hopf operators
• 47B10: Operators belonging to operator ideals (nuclear, p -summing, in the Schatten-von Neumann classes, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2006
• Tom: 175
• Numer: 2
• Strony: 175-204

Daty

wydano

2006

Twórcy

autor

Aleksander Pełczyński

• Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00-956 Warszawa, Poland

autor

Fyodor Sukochev

• School of Informatics and Engineering, Flinders University of South Australia, 5042 Bedford Park, Australia

Identyfikatory

DOI

10.4064/sm175-2-5