Comptes Rendus
no. 1-2
Functional Analysis
A characterization of upper triangular trace class matrices

Presented by: 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.

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.

Received:
Accepted:
Published online:
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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