The s-numbers of Schatten class embeddings

Roughly speaking, the s-numbers of a linear operator between two Banach spaces are certain quantities which indicate how compact this operator is. One can introduce various sequences of s-numbers (classical examples include the approximation and Gelfand numbers of an operator). Then one can wonder what the asymptotic behavior of these s-numbers is in the case when we have a nice and simple linear operator between two nice and classical Banach spaces.

In the talk I will introduce all the necessary preliminaries about s-numbers and then explain which techniques can be used to find the asymptotic behavior of the s-numbers of the embedding \ell_p^N \to \ell_q^N. In the last part we will discuss what changes when we look at the s-numbers of the embeddings of Schatten classes. (Some probabilistic accents will appear).