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Our main aim is to prove the following theorem. If X is a barrelled locally
convex space, and
the unital algebra homomorphism m from C(K) into L(X) is continuous with respect to the norm topology on C(K) and the strong operator toplogy on L(X), then the weak operator topology closure of m(C(K)) is a reflexive operator algebra. This generalizes Theorem 7 in [12]. As a consequence of this result, it is shown that the weak operator topology closure of the linear span of an equicontinuous Boolean algebra B of projections in the quasi-complete barrelled locally convex space X is AlgLat (B) |