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  3. let {λn} be a sequence of scalars that converge

Let {λn} be a sequence of scalars that converges to zero, limn→∞ λn = 0. Show...

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Advance Math

Let {λn} be a sequence of scalars that converges tozero, limn→∞ λn = 0. Show that the operator A: ℓ2 → ℓ2 , A(x1, x2,..., xn, ...) = (λ1x1,λ2x2, ..., λnxn, ...)is compact. What is the spectrum of this operator?

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