On sums and products of unbounded operators in Hilbert space
M. J. J. Lennon · Transactions of the American Mathematical Society · 1974
The characteristic matrices (in the sense of Stone) of the sum and product of two closed linear operators in Hilbert space are found in terms of the characteristic matrix of each operator. From these, necessary and sufficient conditions for the domain of the sum or product to be dense are found, and a new simple condition for the density of the domain of the sum is proved. The ideas developed are applied to the direct integral decomposition of closed linear operators.