Suppose that akj > 0 for k, j N. Set for each k N, and suppose that

Suppose that akj > 0 for k, j ˆˆ N. Set

for each k ˆˆ N, and suppose that ˆ‘ˆžk=1 Ak converges.
a) Prove that

b) Show that

c) Prove that b) may not hold if akj has both positive and negative values.
Consider

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i j-k 0 otherwise.