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Abstrakty
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.
Słowa kluczowe
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.)
Czasopismo
Rocznik
Tom
Numer
Strony
175-204
Opis fizyczny
Daty
wydano
2006
Twórcy
autor
- Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00-956 Warszawa, Poland
autor
- School of Informatics and Engineering, Flinders University of South Australia, 5042 Bedford Park, Australia
Bibliografia
Typ dokumentu
Bibliografia
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Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_4064-sm175-2-5