Eigenvalues and s-numbers
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We prove asymptotic formulas for the behavior of approximation quantities of identity operators between symmetric sequence spaces. These formulas extend recent results of Defant, Mastylo, and Michels for identities lpn←Fn with an n-dimensional symmetric normed space Fn with p-concavity conditions on Fn and 1 ≤ p ≤ 2. We consider the general case of identities En←Fn with weak assumptions on the asymptotic behavior of the fundamental sequences of the n-dimensional symmetric spaces En and Fn. We give applications to Lorentz and Orlicz sequence spaces, again considerably generalizing results of Pietsch, Defant, Mastylo, and Michels.