Comptes Rendus
no. 1-2
Functional Analysis
A characterization of upper triangular trace class matrices
[Une caractérisation de la classe des matrices supérieurement triangulaires à trace]

Présenté par : Gilles Pisier

Nicolae Popa1, 2
1 Faculty of Mathematics and Informatics, University of Bucharest, Romania
2 Institute of Mathematics, Romanian Academy, P.O. Box 764, 014700 Bucharest, Romania
Comptes Rendus. Mathématique, Volume 347 (2009) no. 1-2, pp. 59-62.

On donne une caractérisation de la classe des matrices supérieurement triangulaires à trace comme une conséquence de l'inégalité vectorielle de Hardy. Cette caractérisation est complètement similaire de celle valable por les espaces de Hardy.

As a consequence of the vector-valued Hardy inequality it is given a characterization of upper triangular trace class matrices completely similar to that of classical Hardy space of analytic functions H1, as may be found for instance in Pavlović's book.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2008.11.020

Nicolae Popa 1, 2

1 Faculty of Mathematics and Informatics, University of Bucharest, Romania
2 Institute of Mathematics, Romanian Academy, P.O. Box 764, 014700 Bucharest, Romania 
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Nicolae Popa. A characterization of upper triangular trace class matrices. Comptes Rendus. Mathématique, Volume 347 (2009) no. 1-2, pp. 59-62. doi : 10.1016/j.crma.2008.11.020. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2008.11.020/

[1] O. Blasco; A. Pelczynski Theorems of Hardy and Paley for vector valued analytic functions and related classes of Banach spaces, Trans. Amer. Math. Soc., Volume 323 (1991), pp. 335-367

[2] O.C. McGehee; L. Pigno; B. Smith Hardy's inequality and the L1 norm of exponential sums, Ann. of Math., Volume 113 (1981), pp. 613-618

[3] M. Pavlović, Introduction to function spaces on the disk, Matematicki Institut SANU, Beograd, 2004

[4] B. Smith A strong convergence theorem for H1(T), Storrs, CT, 1980/1981 (Lecture Notes in Math.), Volume vol. 995, Springer-Verlag, Berlin (1983), pp. 169-173

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