B737 ON FINAL FOR LAX EXPERIENCED RA WITH B757; CTLR ERROR.

Narrative

ON THE PARADISE FOUR ARR (RNAV); WE WERE CLRED TO 'DSCNT VIA THE POZ4 ARR TO RWY 24R.' APCHING MITTS; SOCAL POINTED OUT ACFT Y TFC 1 O'CLOCK POS FOR ABOUT 2 MI AND THAT HE HAD US IN SIGHT. WE RESPONDED THAT WE HAD HIM IN SIGHT. HE WAS NOT ON OUR FREQ. WE WERE SLOWING CONVERGING AND CAREFULLY WATCHING HIM VISUALLY AND ON TCASII. HE WAS ALMOST 1000 FT HIGHER AND I THOUGHT PERHAPS HE WAS ON A VECTOR TO JOIN FINAL FOR RWY 25L OR R. AS WE REACHED MITTS AT 10000 FT MSL; WE EXPEDITIOUSLY RESET OUR ALT TO 8000 FT FOR DENAY AND PUSHED OVER; SINCE THE B757 WAS NOW ONLY ABOUT 800 FT ABOVE OUR ALT. DURING THIS TIME; I WAS ANXIOUS FOR A CHANCE TO QUERY SOCAL ABOUT THEIR INTENTIONS FOR THE B757; BUT COULD NOT BECAUSE THE FREQ WAS CONTINUOUSLY BUSY FOR AT LEAST A FULL MIN AS WE CONVERGED. I PUSHED IDENT ON OUR XPONDER AS WE PUSHED OVER OUT OF 10000 FT MSL. THE B757 EVIDENTLY INCREASED HIS DSCNT RTE BECAUSE WE NEXT GOT AN RA TO DSND WITH VERT SPACING APPROX 400 FT AND ABOUT 1/2 MI HORIZ SPACING. AT THIS POINT; IT WAS OBVIOUS THE B757 WAS GOING TO THE SAME LOC RWY 24R. BEFORE WE HAD A CHANCE TO CALL THEM; SOCAL ISSUED US A L TURN TO 180 DEGS AND DSCNT CLRNC TO 4000 FT. WITH OUR ACKNOWLEDGEMENT; WE INFORMED THEM OF OUR RA DSCNT. SOCAL SAID ACR Y HAD RELAYED HIS RA CLB AND SOME WORDS ABOUT ACFT Y 'NOT BEING TOO HAPPY.' I ELECTED TO ASK FOR A TELEPHONE NUMBER FOR SOCAL; WHICH I THINK IS MORE PROFESSIONAL. SOCAL PROMISED A TELEPHONE NUMBER 'PRIOR TO LNDG.' ABOUT 30 SECONDS LATER; SOCAL RECLRED US TO INTERCEPT LOC RWY 25L AND APOLOGIZED FOR ANY CONFUSION; INTIMATED THAT THE CONFLICT WAS THEIR MISTAKE; AND PROMISED A TELEPHONE NUMBER FROM GND CTL. LANDED RWY 25L UNEVENTFULLY. AT THE GATE; I CALLED THE MGR ATC SYS. HE WANTED TO CALL SOCAL FIRST; SO I DID NOT. HE CALLED ME BACK ABOUT 10 MINS LATER SAYING SOCAL HAD LISTENED TO THE TAPES. WE DID NOTHING WRONG; AND SOCAL APOLOGIZED FOR 'MIS-SPEAKING' OUR RWY ASSIGNMENT ON OUR INITIAL CLRNC WHILE ON THE PDZ4. THEY HAD INTENDED TO PUT US ON RWY 25L. WE WERE NEVER ON THE SAME FREQ AS ACFT Y.