Approximate modularity: Kalton's constant is not smaller than 3

0537553 - MÚ 2022 RIV US eng J - Článek v odborném periodiku
Gnacik, M. - Guzik, M. - Kania, Tomasz
Approximate modularity: Kalton's constant is not smaller than 3.
Proceedings of the American Mathematical Society. Roč. 149, č. 2 (2021), s. 661-669. ISSN 0002-9939. E-ISSN 1088-6826
Grant CEP: GA ČR(CZ) GJ19-07129Y
Institucionální podpora: RVO:67985840
Klíčová slova: 1-additive set function * Kalton's constant * Ulam-Hyers stability * approximate modularity
Obor OECD: Pure mathematics
Impakt faktor: 0.971, rok: 2021
Způsob publikování: Omezený přístup
https://doi.org/10.1090/proc/15195

Kalton and Roberts [Trans. Amer. Math. Soc., 278 (1983), 803–816] proved that there exists a universal constant K 6 44:5 such that for every set algebra F and every 1-additive function f : F ! R there exists a finitely additive signed measure defined on F such that jf(A) 􀀀 (A)j 6 K for any A 2 F. The only known lower bound for the optimal value of K was found by Pawlik [Colloq. Math., 54 (1987), 163–164], who proved that this constant is not smaller than 1:5, we improve this bound to 3 already on a non-negative 1-additive function. Recently, Feige, Feldman, and Talgam-Cohen decreased an upper estimate for K to 24 [SIAM J. Comput., 49 (2020), 67–97] and drew a connection between better estimation of Kalton’s constant and enhancing various optimisation algorithms, we improve another constant related to approximately modular functions considered ibid.
Trvalý link: http://hdl.handle.net/11104/0315371