Coincidence and Calculation of some Strict $s$-Numbers

Abstract

The paper considers the so-called strict $s$-numbers, which form an important subclass of the family of all $s$-numbers. For operators acting between Hilbert spaces the various $s$-numbers are known to coincide: here we give examples of linear maps $T$ and non-Hilbert spaces $X,Y$ such that all strict $s$-numbers of $T:X\to Y$ coincide. The maps considered are either simple integral operators acting in Lebesgue spaces or Sobolev embeddings; in these cases the exact value of the strict $s$-numbers is determined.