THE EIGENVALUE DISTRIBUTION OF A HUBERT-SCHMIDT-TYPE OPERATOR

Abstract

We prove the following theorem in answer to a question raised by P Nowosad and R Tovar in 3]. If K is a kernel operator on L²(x,u) with kernel K(x, y) if P(x): = U_X |K(x, y)|² d μ(y))½ and Q(x): = (U_X |K (y, x)|² d μ(y))½ and if _x PQdμ < ∞, then σ|λ_i|² < ∫_X PQd μ where (λ_i) is the se = zuence of eigenvalues of K.