That looks like it was originally anodised? Maybe get it redone?
Unless the oxidation is very heavy, just use a proprietary aluminium polish, as used for car wheels etc. Expect to have to keep polishing into the future unless you seal the surface with a suitable sealer. Google will come up with polishes and sealers.
Generally unfinished aluminium alloys will always oxidise, some faster than others. I’ve only ever seen door handles, that get constant use, keep a bright finish without polishing, and then only on some surfaces.
Neil