科研之友
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摘要
Suppose E, F, G are locally convex spaces, b: E x F -> G is a bilinear operator and lambda is a scalar sequence space. A series Sigma(j)x(j) in E is lambda b multiplier convergent if for every t = {t(j)} is an element of lambda there exists x(t) is an element of E such that Sigma(infinity)(j=1) t(j)b(x(j), y) = b(x(t), y) for every y is an element of F. Under continuity assumptions on the linear operators b(x, .), we establish several versions of the Orlicz-Pettis Theorem for multiplier convergent series. Applications to spaces of continuous linear operators are given.
