By a diagonal minus tail form (of even degree) we understand a real homogeneous polynomial F(x1, . . . , xn) = F(x) = D(x) − T(x), where the diagonal part D(x) is a sum of terms of the form $${b_i… Expand

We present several new Young-type inequalities for positive real numbers and we apply our results to obtain the matrix analogues. Among others, for real numbers , and , with and , we prove the… Expand

Abstract Let X,Y be matrices of spectra x 1 ,…, x n and y 1 ,…, y n , respectively. For a wide class of pairs of essentially Hermitian matrices X,Y , we prove that the determinant of X+Y belongs to… Expand

A complete solution is presented for the problem of determining the sets of points at which the functions (x1, . . . , xn) → xk + . . . + xl, subject to the constraints M x1 . . . xn m, x1 + x2 + . .… Expand

Abstract We prove an identity for the Cartan invariants of the Schur algebra S(B+) using combinatorial properties of row semistandard λ-tableaux. The problem arose in connection with the construction… Expand