Diagonals of operators and pinching
Let T be a bounded linear operator on a separable Hilbert space H. We will discuss the question what are the possible diagonals (<Tek,ek>) of T with respect to an orthonormal basis (ek) in H. The question will be also discussed for n-tuples of operators, especially for n-tuples of the form (T,T2,…,Tn) where T ∈ B(H).
Similar techniques give also new results for the “pinching” of operators.
The talk is based on joint work with Yu. Tomilov.