We derive the peak luminosity - peak energy (L_iso - E_peak) correlation using 22 long Gamma-Ray Bursts (GRBs) with firm redshift measurements. We find that its slope is similar to the correlation between the time integrated isotropic emitted energy E_iso and E_peak (Amati et al. 2002). For the 15 GRBs in our sample with estimated jet opening angle we compute the collimation corrected peak luminosity L_gamma, and find that it correlates with E_peak. This has, however, a scatter larger than the correlation between E_peak and E_gamma (the time integrated emitted energy, corrected for collimation; Ghirlanda et al. 2004), which we ascribe to the fact that the opening angle is estimated through the global energetics. We have then selected a large sample of 442 GRBs with pseudo--redshifts, derived through the lag-luminosity relation, to test the existence of the L_iso-E_peak correlation. With this sample we also explore the possibility of a correlation between time resolved quantities, namely L_iso,p and the peak energy at the peak of emission E_peak,p.
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