Products of Cesàro Convergent Sequences with Applications to Convex Solid Sets and Integral Operators
نویسنده
چکیده
Let 0 ≤ an, bn, cn such that an = bncn. If a = limn→∞ an, and {bn} and {cn} Cesàro converge to b, respectively c, then a ≤ bc. This implies that if in addition {bn} and {cn} are similarly ordered, then a = bc. As applications we prove that the pointwise product of two convex solid sets closed in measure is again closed in measure and a factorization result for kernels of regular integral operators on Lp–spaces.
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تاریخ انتشار 2008