A B757 CREW HAD LTSS WITH A VFR PA28 IN ZLA CLASS E AIRSPACE.

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WHILE DSNDING FOR ARR INTO SAN; WE EXPERIENCED A POTENTIAL ALT CONFLICT WITH OPPOSITE DIRECTION VFR TFC WHILE UNDER ZLA CTL. WE WERE GIVEN CLRNC TO CROSS PILLO INTXN AT 10000 FT. JUST PAST PILLO; CTR ADVISED US OF OPPOSITE DIRECTION TFC AT 9500 FT. WX CONDITIONS WERE VFR ON TOP; WITH TOPS AT 8500 FT. TFC WAS PIPER CHEROKEE OPPOSITE DIRECTION AT 20 MI W. WE OBSERVED TFC ON TCASII INITIALLY; INDICATING -200 FT FROM OUR CURRENT ASSIGNED ALT OF 10000 FT. I QUERIED ATC TO VERIFY ALT OF APCHING TFC. ZLA CTLR INFORMED CHEROKEE HIS DISPLAY SHOWED HIM AT 9800 FT. CHEROKEE RESPONDED THAT HE WAS AT 9600 FT. AT 5 MI; WE DEVIATED TO 10300 FT WITH A SUBSEQUENT TCASII RA INDICATING NOT TO DSND; AND INFORMED CTR OF TCASII CLB. WE HAD VISUAL OBSERVATION OF TFC APCHING HEAD ON 5 MI RANGE. TCASII NOW INDICATING TFC AT -500 FT WHILE WE WERE AT 10300 FT. WE PASSED OVERHEAD TFC AT 10300 FT WITH 500 FT ALT DIFFERENCE INDICATED ON TCASII. WITHOUT TCASII AND DEV ON OUR PART; WE WOULD HAVE HAD A NEAR MISS AND POTENTIAL CONFLICT.