**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 (<Te_{k},e_{k}>) of T with respect to an orthonormal basis (e_{k}) in H. The question will be also discussed for n-tuples of operators, especially for n-tuples of the form (T,T^{2},…,T^{n}) 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.