The electronic structures of UX$_3$ (X=Al, Ga, and In) were studied by photoelectron spectroscopy to understand the relationship between their electronic structures and magnetic properties. The band structures and Fermi surfaces of UAl$_3$ and UGa$_3$ were revealed experimentally by angle-resolved photoelectron spectroscopy (ARPES), and they were compared with the result of band-structure calculations. The topologies of the Fermi surfaces and the band structures of UAl$_3$ and UGa$_3$ were explained reasonably well by the calculation, although bands near the Fermi level ($E_mathrm{F}$) were renormalized owing to the finite electron correlation effect. The topologies of the Fermi surfaces of UAl$_3$ and UGa$_3$ are very similar to each other, except for some minor differences. Such minor differences in their Fermi surface or electron correlation effect might take an essential role in their different magnetic properties. No significant changes were observed between the ARPES spectra of UGa$_3$ in the paramagnetic and antiferromagnetic phases, suggesting that UGa$_3$ is an itinerant weak antiferromagnet. The effect of chemical pressure on the electronic structures of UX$_3$ compounds was also studied by utilizing the smaller lattice constants of UAl$_3$ and UGa$_3$ than that of UIn$_3$. The valence band spectrum of UIn$_3$ is accompanied by a satellite-like structure on the high-binding-energy side. The core-level spectrum of UIn$_3$ is also qualitatively different from those of UAl$_3$ and UGa$_3$. These findings suggest that the U~$5f$ states in UIn$_3$ are more localized than those in UAl$_3$ and UGa$_3$.
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