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

Let {λ_n} be a sequence of scalars that converges to zero, lim_n→∞ λ_n = 0. Show that the operator A : ℓ² → ℓ² , A(x₁, x₂, ..., x_n, ...) = (λ₁x₁, λ₂x₂, ..., λ_nx_n, ...) is compact. What is the spectrum of this operator?

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Colby Messinger answered 1 year ago

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