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Our goal is to study the evolution of the $B-$band luminosity function (LF)since $z=1$ using ALHAMBRA data. We used the photometric redshift and the$I-$band selection magnitude probability distribution functions (PDFs) of thoseALHAMBRA galaxies with $I\leq24$ mag to compute the posterior LF. Westatistically studied quiescent and star-forming galaxies using the templateinformation encoded in the PDFs. The LF covariance matrix inredshift-magnitude-galaxy type space was computed, including the cosmicvariance. That was estimated from the intrinsic dispersion of the LFmeasurements in the 48 ALHAMBRA sub-fields. The uncertainty due to thephotometric redshift prior is also included in our analysis. We modelled the LFwith a redshift-dependent Schechter function affected by the same selectioneffects than the data. The measured ALHAMBRA LF at $0.2\leq z<1$ and theevolving Schechter parameters both for quiescent and star-forming galaxiesagree with previous results in the literature. The estimated redshift evolutionof $M_B^* \propto Qz$ is $Q_{\rm SF}=-1.03\pm0.08$ and $Q_{\rmQ}=-0.80\pm0.08$, and of $\log \phi^* \propto Pz$ is $P_{\rm SF}=-0.01\pm0.03$and $P_{\rm Q}=-0.41\pm0.05$. The measured faint-end slopes are $\alpha_{\rmSF}=-1.29\pm0.02$ and $\alpha_{\rm Q}=-0.53\pm0.04$. We find a significantpopulation of faint quiescent galaxies, modelled by a second Schechter functionwith slope $\beta=-1.31\pm0.11$. We find a factor $2.55\pm0.14$ decrease in theluminosity density $j_B$ of star-forming galaxies, and a factor $1.25\pm0.16$increase in the $j_B$ of quiescent ones since $z=1$, confirming the continuousbuild-up of the quiescent population with cosmic time. The contribution of thefaint quiescent population to $j_B$ increases from 3% at $z=1$ to 6% at $z=0$.The developed methodology will be applied to future multi-filter surveys suchas J-PAS.

The ALHAMBRA survey : $B-$band luminosity function of quiescent and star-forming galaxies at $0.2 \leq z < 1$ by PDF analysis