GJ 9827 is a bright star hosting a planetary system with three transiting planets. As a multiplanet system with planets that sprawl within the boundaries of the radius gap between terrestrial and gaseous planets, GJ 9827 is an optimal target to study the evolution of the atmospheres of close-in planets with a common evolutionary history and their dependence from stellar irradiation. Here we report on the Hubble Space Telescope (HST) and CARMENES transit observations of GJ 9827 planets b and d. We performed a stellar and ISM characterization from the ultraviolet HST spectra, obtaining fluxes for Lyα and Mg II of F(Lyα) = (5.42 ${}_{-0.75}^{+0.96}$ ) × 10-13 erg cm-2 s-1 and F(MgII) = (5.64 ± 0.24) × 10-14 erg cm-2 s-1. We also investigated a possible absorption signature in Lyα in the atmosphere of GJ 9827b during a transit event from HST spectra, as well as Hα and He I signature for the atmosphere of GJ 9827b and d from CARMENES spectra. We found no evidence of an extended atmosphere in either of the planets. This result is also supported by our analytical estimations of mass loss based on the measured radiation fields for all three planets of this system, which led to a mass-loss rate of 0.4, 0.3, and 0.1 planetary masses per Gyr for GJ 9827b, c, and d, respectively. These values indicate that the planets could have lost their volatiles quickly in their evolution and probably do not retain an atmosphere at the current stage.