MLG FLC ON VISUAL INTO LAX FINDS THEMSELVES BELLY UP TO COMMUTER TURNING FINAL FOR OTHER RWYS. MAINTAIN VISUAL CONTACT WITH THE SECOND ACFT.

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I WAS CAPT ON FLT FROM SFO TO LAX AS FO FLEW LEG TO LAX. WX WAS CLR; 5 MI VISIBILITY; HAZE WITH W SUN (XX00L) WE WERE CLRED FOR STADIUM VISUAL APCH RWY 24R AFTER WE CALLED PRECEDING ACFT IN SIGHT. ON BASE TURN GEAR WAS LOWER; FLAPS 10 DEGS; SPD 180 KTS. DURING THE START OF TURN TO FINAL I SAW A COMMUTER ACFT ALSO TURNING BASE TO FINAL RWY 25; THIS TFC WAS CO-ALT; BELLY-UP TO US; AND NOT CALLED OUT BY APCH OR TWR. DURING OUR TURN TO FINAL I TOLD FO TO INCREASE BANK AND TURN AS I KEPT TFC IN SIGHT. I MAINTAINED VISUAL CONTACT THROUGHOUT THE TURN TO ASSURE SEPARATION SINCE WE WERE ON DIFFERENT FREQS AND DID NOT KNOW IF THE TFC HAD US IN SIGHT. WE RECEIVED A SINGLE TCASII RA 'MONITOR VERT SPD;' WHILE IN THE TURN. AS WE ROLLED OUT THE FO LINED UP ON CTRLINE AND WE CONTINUED A NORMAL; STABILIZED APCH; CONTACTED TWR AND LANDED NORMALLY. THE FOLLOWING DAY WAS ADVISED OF POSSIBLE LOSS OF SEPARATION FROM OTHER ACFT. ATC HAD SAID NOTHING. CONTRIBUTING FACTORS TO BE CONSIDERED: SUN; HAZE; FOLLOWING PRECEDING ACFT ON VISUAL APCH WITHOUT RWY IN SIGHT; NO CALL BY ATC OF RWY 25 TFC WHILE ON DIFFERENT FREQS; BOTH ACFT BELLY-UP AT SAME POINT IN TURN AT SAME ALT; NEED TO FEEL I HAD TO KEEP TFC IN SIGHT; SCHEDULING MAY BE CONSIDERED A FACTOR (SHUTTLE OPS; 6TH FLT OF THE DAY; 3RD ACFT OF DAY) ALTHOUGH NEITHER THE FO OR MYSELF CONSIDERED OURSELVES FATIGUED.