PVT PLT OF AN SMA SEL LANDS ON A CLOSED RWY DUE TO MISUNDERSTANDING TWR'S INSTRUCTIONS.

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I WAS FLYING TO BKL FROM THE W ALONG THE SHORELINE. I LISTENED TO ATIS INFO. WINDS WERE CALM AND BKL WAS LNDG RWYS 24R AND 6L. THE ATIS STATED THAT CERTAIN SECTIONS OF RWY 24L COULD BE USED TO TAXI TO TERMINAL AREA AND THAT ALL OTHER AREAS WERE CLOSED TO TRANSIENT TFC. IT ALSO GAVE CAUTIONS ABOUT ENTERING CLASS B AIRSPACE AT CLEVELAND HOPKINS ARPT. THE WX WAS VFR; HIGH CIRRUS CLOUDS; FLT VISIBILITY BETTER THAN 10 MI; NEGATIVE TURB. I RADIOED BKL ABOUT 10 MI OUT WITH ATIS INFO. THE CTLR ASKED ME TO RPT 2 MI W FOR R DOWNWIND FOR RWY 24R. I CALLED THAT POS AND STARTED DOWNWIND. THE CTLR ACKNOWLEDGED. THE CTLR THEN ASKED ME; I THOUGHT; IF I WANTED TO USE RWY 24R OR 24L. I SAID I WOULD TAKE RWY 24L TO THE BEST OF MY REMEMBRANCE. THE XMISSION AGAIN WAS ACKNOWLEDGED BY THE CTLR. THE LNDG LIGHT WAS ON WHEN TURNING BASE TO FINAL FOR RWY 24L. I LANDED RWY 24L WITHOUT INCIDENT. THE CTLR THEN ASKED ME WHERE I WAS. I SAID I WAS ON RWY 24L. THE CTLR SAID RWY 24L WAS CLOSED; AND TO GIVE THE TWR A PHONE CALL AFTER I PARKED AT THE TERMINAL. THE CTLR; OVER THE PHONE; SAID THIS WOULD POSSIBLY BE A MINOR INFRACTION. I SAID I THOUGHT I WAS CLRED TO LAND RWY 24L. I DON'T REMEMBER IF THE CTLR MAY HAVE GIVEN ME THE OPTION TO LAND RWY 6L OR RWY 24R; BUT I WAS ALREADY DOWNWIND FOR RWY 24R AT THE TIME THE QUESTION WAS ASKED AND THOUGHT THE OPTION WAS RWY 24L. THE ATIS NEVER CLRLY STATED THAT RWY 24L WAS CLOSED TO LNDG TRANSIENT ACFT. ALL IT SAID WAS THAT IT WAS USED FOR TAXI AND ALL OTHER AREAS WERE CLOSED. ALSO FOR SOME REASON THE CTLR LOST TRACK OF ME IN THE PATTERN. THE TWR HAS GOOD VISIBILITY OF THE ARPT FROM ALL DIRECTIONS.