Seminarium KMMF "Teoria Dwoistości"

Little Grothendieck's Theorem in one of its version states that any bounded linear operator between Hilbert spaces which admits factorization through L^1 space is a Hilbert-Schmidt operator. During the presentation we will consider a possible generalization of this theorem for translation invariant operators on torus which admit invariant factorization through anisotropic Sobolev space. We will show that such operators belong to some non-trivial Schatten class.