Abstract
Let SNr (r ≥ 1) denote the Schatten-von Neumann ideal of compact operators in a separable Hilbert space. For the block matrix
the inequality
(p = 2; 3; … ) is proved, where λk(A) (k = 1; 2; … ) are the eigenvalues of A and Nr(.) is the norm in SNr. Moreover, let P(z) = z2I + Bz + C (z ∈ ℂ) with B ∈ SN2p, C ∈ SNp. By zk(P) (k = 1; 2; … ) the characteristic values of the pencil P are denoted. It is shown that
In the case p = 1, sharper results are established. In addition, it is derived that