Abstract
We prove asymptotic formulas for the behavior of approximation quantities of identity operators between symmetric sequence spaces. These formulas extend recent results of Defant, Mastyło, and Michels for identities l p n↪F n with an n-dimensional symmetric normed space F n with p-concavity conditions on F n and 1⩽ p⩽2. We consider the general case of identities E n↪F n with weak assumptions on the asymptotic behavior of the fundamental sequences of the n-dimensional symmetric spaces E n and F n . We give applications to Lorentz and Orlicz sequence spaces, again considerably generalizing results of Pietsch, Defant, Mastyło, and Michels.
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