In this paper we continue and refine a discussion begun concerning the continuation properties of the non-cyclic vectors for the backward shift operator Bf=f-f(o)/z on a general Banach space X contained in Hol(D), the analytic functions on the open unit disk D:=. Here we say fEX is cyclic if /f/:=VB (sup n) f: n=0,1,2>=X (V denotes the closed linear span).
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