[Aims]: Our goal is to study the evolution of the B-band luminosity function (LF) since z ∼ 1 using ALHAMBRA data. [Methods]: We used the photometric redshift and the I-band selection magnitude probability distribution functions (PDFs) of those ALHAMBRA galaxies with I ≤ 24 mag to compute the posterior LF. We statistically studied quiescent and star-forming galaxies using the template information encoded in the PDFs. The LF covariance matrix in redshift - magnitude - galaxy type space was computed, including the cosmic variance. That was estimated from the intrinsic dispersion of the LF measurements in the 48 ALHAMBRA sub-fields. The uncertainty due to the photometric redshift prior is also included in our analysis. [Results]: We modelled the LF with a redshift-dependent Schechter function affected by the same selection effects than the data. The measured ALHAMBRA LF at 0.2 ≤ z < 1 and the evolving Schechter parameters both for quiescent and star-forming galaxies agree with previous results in the literature. The estimated redshift evolution of M ∝ Q is Q = -1.03±0.08 and Q = -0.80±0.08, and of logφ ∝ P is P = -0.01±0.03 and P = -0.41 ± 0.05. The measured faint-end slopes are α = -1.29 ± 0.02 and α = -0.53 ± 0.04. We find a significant population of faint quiescent galaxies with M ≳ -18, modelled by a second Schechter function with slope β = -1.31 ± 0.11. [Conclusions]: We present a robust methodology to compute LFs using multi-filter photometric data. The application to ALHAMBRA shows a factor 2.55 ± 0.14 decrease in the luminosity density j of star-forming galaxies, and a factor 1.25 ± 0.16 increase in the j of quiescent ones since z = 1, confirming the continuous build-up of the quiescent population with cosmic time. The contribution of the faint quiescent population to j increases from 3% at z = 1 to 6% at z = 0. The developed methodology will be applied to future multi-filter surveys such as J-PAS. ; This work has been mainly funded by the FITE (Fondos de Inversiones de Teruel) and the projects AYA2015-66211-C2-1, AYA2012-30789, AYA2006-14056, and CSD2007-00060. We also acknowledge support from the Spanish Ministry for Economy and Competitiveness and FEDER funds through grants AYA2010-15081, AYA2010-15169, AYA2010-22111-C03-01, AYA2010-22111-C03-02, AYA2011-29517-C03-01, AYA2012-39620, AYA2013-40611-P, AYA2013-42227-P, AYA2013-43188-P, AYA2013-48623-C2-1, AYA2013- 48623-C2-2, ESP2013-48274, AYA2014-58861-C3-1, Aragón Government Research Group E103, Generalitat Valenciana projects Prometeo 2009/064 and PROMETEOII/2014/060, Junta de Andalucía grants TIC114, JA2828, P10-FQM-6444, and Generalitat de Catalunya project SGR-1398. E.T. acknowledges the support by the ETAg grants IUT26-2, IUT40-2, and by the European Regional Development Fund (TK133). A.M. acknowledges the financial support of the Brazilian funding agency FAPESP (Post-doc fellowship – process number 2014/11806-9). B.A. has received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No. 656354. ; Peer Reviewed
