Norm Attaining Elements of the Ball Algebra H-infinity(B-N)

Abstract

[EN] Let B(N )be the Euclidean ball of C-N. The space H-infinity(B-N) of bounded holomorphic functions on B-N is known to have a predual, denoted by G(infinity)(B-N). We study the functions in H-infinity(B-N) that attain their norm as elements of the dual of G(infinity)(B-N). We also examine similar questions for the polydisc algebra H-infinity(D-N) and for the space of Dirichlet series D-infinity(C+).The authors are very grateful to the referee for the careful reading of our manuscript and for the suggestions which improved our article. The research of R. Aron was partially supported by the project PID2021-122126NB-C33/MCIN/AEI/ 10.13039/ 501100011033 (FEDER). The research of J. Bonet was partially supported by the project PID2020-119457GB-100 funded by MCIN/AEI/10.13039/501100011033 and by "ERFD A way of making Europe" and by the project GV AICO/2021/170. The research of M. Maestre was partially supported by the project PID2021-122126NB-C33/MCIN/AEI/10.13039/501100011033 (FEDER) and the project GV PROMETEU/2021/070.Aron, RM.; Bonet Solves, JA.; Maestre, M. (2024). Norm Attaining Elements of the Ball Algebra H-infinity(B-N). Results in Mathematics. 79(2). https://doi.org/10.1007/s00025-023-02111-179