Santa Barbara Bancorp, the holding company for Santa Barbara Bank & Trust and Lompoc-based First Valley Bank, said they have signed a definitive merger agreement. The deal is valued at $26.1 million. The agreement would give shareholders of the closely held First Valley Bank $58 in cash for each of the 450,000 First Valley Bank shares outstanding. First Valley Bank has three offices in the Lompoc area, one in Santa Maria, and one in Los Olivos. All of the offices would remain open as branches of Santa Barbara Bank & Trust. The merger would give Santa Barbara Bank a total of 20 offices, extending its service area from Camarillo north to Santa Maria. The merger is expected to close at the end of the first quarter of 1997, subject to regulatory approval and the approval of First Valley Bank shareholders. Santa Barbara Bancorp shares lost 75 cents to close at $27.875 on Nasdaq.