LAX87FA156

While flying northwest over water along the pacific coast on an IFR clnc, the plt rprtd to the sector controller (ctlr) 'we've got a problem.' The ctlr inquired about the nature of the problem. The plt then stated, 'going down fast, out of control.' The ctlr observed that the acft was losing alt rapidly & instructed the plt to turn right to 090 deg for vectors toward the shoreline; the plt responded, 'we're going in.' No further transmissions were received from the plt. The ctlr noted the acft's transponder code went into a coast mode & the primary target went into a slow left turn. Radar contact was lost with the acft after it had turned to a southwesterly heading. Coast guard helicopters arrived over the area of the acdnt at about 1700 PST. The helicopter aircrews found an oil slick, a lndg gear & other remnants of the acft; however, the major portion of the acft sank & was not recovered.