ZLA CTLR TAKES EVASIVE CTL ACTIONS WITH AN E120 AFTER AFFECTING COORD WITH ADJOINING SECTOR WITH CONFLICTING TFC.

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I WAS WORKING ACR W AT FL190. I HAD RECEIVED THE HDOF FROM SECTOR R21 WHO TOLD ME ACR W WAS REQUESTING DIRECT BZA. IT WAS NOT IN THE COMPUTER AND HE WAS MY CTL REF ACR X. I HAD A POINTOUT ON ACR X AND WHEN ACR X LEFT FL210; I CLBED ACR W TO FL210. I TOLD R21 I WAS TURNING THE ACR W TO BZA AND ISSUED A 130 DEG HDG TO KEEP AWAY FROM ACR Y OVER PDZ. THEN I GOT A POINTOUT ON AN ACR Z STOPPED AT FL200. I TOLD ACR W TO IMMEDIATELY DSND AND MAINTAIN FL190 AND TURNED ACR W BACK TO 080 DEGS AWAY FROM THE ACR Z I ISSUED TFC. THE ACR W MODE C READ 19800 FT THEN STARTED DSNDING. THE ACFT GOT NO CLOSER THAN 5-6 MI; AND 200 FT VERTLY. CONFLICT ALERT DID ACTIVATE AND ACR W SAID HE HAD THE ACR Z ON TCASII. THIS WAS NOT AN OPERROR BUT COULD HAVE BEEN. THE SECTOR 21 CTLR WAS NEW AND HAD BEEN SIGNED OFF ON THE SECTOR ONLY A MATTER OF DAYS. HIS SUPVR WAS STANDING BEHIND HIM TELLING HIM WHAT TO DO; INSTEAD OF PUTTING ANOTHER CTLR IN TO WORK. THE NEW CTLR WAS FINALLY RELIEVED. I BELIEVE POOR JUDGEMENT ON THE SUPVR'S PART CONTRIBUTED TO THIS SIT. SECTOR 21 WAS COMBINED WITH SECTOR 22 WHICH IS THE WAY IT IS NORMALLY RUN; AT TIMES DANGEROUSLY; PLUS THE RADAR RESOLUTION WAS POOR WITH CLUTTER. SUPPLEMENTAL INFO FROM ACN 434190: WE WERE ACR W AND A SIMILAR SOUNDING CALL SIGN; COMPANY ACR X WAS ALSO ON FREQ. WE HAD JUST BEEN HANDED OFF TO ZLA; AND ON INITIAL CONTACT WE REQUESTED FL210 AND DIRECT BZA OR IPL (VOR) IF POSSIBLE. THE CTLR SOON AFTER; GAVE US A 130 DEG HDG AND TOLD US TO CLB TO FL210. WHEN COMPANY ACR X ASKED FOR DIRECT IPL; SHE (THE CTLR) SEEMED PUZZLED BY THIS REQUEST AND QUERIED THEM. SHE SEEMED VERY BUSY AND A BIT OVERLOADED. SHE THEN MADE A CALL TO US AND TOLD US TO STOP OUR CLB AND DSND IMMEDIATELY TO FL190 AND RPTED TFC AT OUR 3 O'CLOCK POS. WE SHOULD HAVE QUESTIONED THE CTLR WHEN SHE SEEMED CONFUSED BTWN US AND OUR COMPANY ACFT. BUT AT THE TIME SHE WAS SO BUSY; I DON'T THINK WE COULD HAVE GOTTEN A WORD IN.