Comptes Rendus
no. 19-20
Mathematical Analysis/Functional Analysis
(e)-convergence and related problem
[(e)-convergence et problème connexe]

Présenté par : Gilles Pisier

Mübariz Tapdıgoğlu Karaev1
1 Isparta Vocational School, Suleyman Demirel University, 32260, Isparta, Turkey
Comptes Rendus. Mathématique, Volume 348 (2010) no. 19-20, pp. 1059-1062.

On donne une réponse négative à une question posée par Zobroska (2003) dans [13] ; cette question porte sur le comportement à la frontière des symboles de Berezin d'opérateurs spaciaux de Bergman. On introduit aussi les notions de (e)-sommabilité de suites et de séries de nombres complexes et on étudie certaines de leurs propriétés. Comme corollaire, on retrouve les théorèmes classiques de Abel sur la théorie de la sommabilité.

We answer negatively to a question of Zorboska (2003) [13], which is concerned to the boundary behavior of Berezin symbols of Bergman space operators. We also introduce the notions of (e)-summability of sequences and series of complex numbers, and study some of their properties. As a corollary, we obtain the classical Abel theorems of summability theory.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2010.09.017
Mübariz Tapdıgoğlu Karaev 1

1 Isparta Vocational School, Suleyman Demirel University, 32260, Isparta, Turkey 
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     title = {(\protect\emph{e})-convergence and related problem},
     journal = {Comptes Rendus. Math\'ematique},
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Mübariz Tapdıgoğlu Karaev. (e)-convergence and related problem. Comptes Rendus. Mathématique, Volume 348 (2010) no. 19-20, pp. 1059-1062. doi : 10.1016/j.crma.2010.09.017. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2010.09.017/

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[9] H. Hedenmalm; B. Korenblum; K. Zhu Theory of Bergman Spaces, Springer Verlag, 2000

[10] M.T. Karaev On some problems related to Berezin symbols, C. R. Acad. Sci. Paris, Volume 340 (2005), pp. 715-718

[11] E. Nordgren; P. Rosenthal Boundary values of Berezin symbols, Oper. Theory Adv. Appl., Volume 73 (1994), pp. 362-368

[12] K. Zhu Operator Theory in Function Spaces, Marcel Dekker, New York, 1990

[13] N. Zorboska The Berezin transform and radial operators, Proc. Amer. Math. Soc., Volume 131 (2003), pp. 793-800

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