NCT Controller described a loss of separation event between a SFO arrival and a SJC departure; the reporter alleging the SFO arrival failed to turn as directed even after three turns were issued.

Narrative

I was working the San Francisco final. I turned a turboprop to a 330 or 310 heading from a northeast bound heading. The pilot acknowledged it but didn't turn right away. I started looking at the next aircraft; and noticed the turboprop didn't turn. I again issued a turn to 310 immediately. The pilot didn't reply; it is possible that the transmission was blocked. I again issued an immediate left turn to 310 to the turboprop (3rd time). He acknowledged it. Around the same time a B737 was departing from SJC. The turboprop and the B737 came within about 2.5 miles of each other; the conflict alert sounded but not until I had taken action to separate the two aircraft. If the turboprop had turned when I told him to; there would have been no loss of separation. I consider this event a pilot deviation. The San Francisco final is busy with arrivals most times of the day. In this example we were in trail; which means delays; a full final for most of the day; well into the night. To work the final you must time your turns at the right moment. What I was doing was normal and appropriate; the turboprop should have turned when I told him.