GA PLT MAKES UNAUTH PENETRATION OF LAX TCA.

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DEP POINT FULLERTON. I DISCUSSED PROC WITH FSS FOR LEAVING LA BASIN VFR. LAX 'CORRIDOR' WAS HIS RECOMMENDATION. 'JUST FOLLOW PROC -- OKAY TO DO.' TWR AT FULLERTON CLRED ME WITH SQUAWK CODE AND COAST CTL FREQ WHERE I SAID I WANTED THE LA CORRIDOR. COAST PICKED ME UP AT ABOUT 1000 FT CLRED ME TO 2500; PASSED ME OFF TO NEXT CTLR WHO CLRED ME TO 4500 FT. I TOLD ONE; OR BOTH; WHAT I WAS DOING; IE; LA 'CORRIDOR.' LAST INSTRUCTION FROM COAST CTL WAS SQUAWK VFR; PROCEED ON COURSE AND RESUME OWN NAV. HAD BEEN VECTORED UP TO THAT TIME. I CAREFULLY FOLLOWED CHARTS THROUGH CORRIDOR -- ASSUMING THAT COAST HAD CLRED ME THROUGH 'CORRIDOR.' MOST OF PATH WAS BELOW TCA BUT RIGHT AT LAX DEP PATH; TCA DROPS FROM 4500 FT TO SEA LEVEL. I REESTABLISHED CONTACT WITH BURBANK FOR FLT FOLLOWING WHEN OUT FROM UNDER TCA AND WAS INFORMED OF POSSIBLE TCA VIOLATION. I WAS PUZZLED AS THE PATH I FLEW WAS EXACTLY AS I THOUGHT COAST HAD TOLD ME TO FOLLOW. IT WAS THEN THAT THE NOTE ON LA TCA VFR CHART BECAME CLR TO ME. CONTACT 124.9(?) ETC; BEFORE FOLLOWING PROC.