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Let 0 < a n ,b n ,c n such that a n = b n c n . If a = lim a→∞ a n , and {b n } and {c n } Cesaro converge to b, respectively c, then a ≤ bc. This implies that if in addition {b n } and {c n } 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.

Products of Cesàro convergent sequences with applications to convex solid sets and integral operators