On some algebraic properties of integral operators (Q1357976)

The author proves two theorems about continuous linear operators. Is \(ABT\) an integral operator for every compact regular integral operator \(A\) in \(L_2\) and every compact Carleman integral operator \(B\) in \(L_2\) then \(T\) is a Hilbert-Schmidt integral operator. The second theorem is analogous, if \(KLTM\) only for compact regular integral operators \(K\) and \(M\) in \(L_2\). Two corollaries for each theorem contain statements about ideals of the set of all integral operators \(L\) and the ideal comprising Hilbert-Schmidt integral operators.