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
Popa, Nicolae1, 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, Tome 347 (2009) no. 1-2, pp. 59-62

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.

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.

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

Popa, Nicolae 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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Popa, Nicolae. A characterization of upper triangular trace class matrices. Comptes Rendus. Mathématique, Tome 347 (2009) no. 1-2, pp. 59-62. doi: 10.1016/j.crma.2008.11.020

[1] Blasco, O.; Pelczynski, A. 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] McGehee, O.C.; Pigno, L.; Smith, B. 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] Smith, B. 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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