Some Remarks on the Algebraic Sum of Unbounded Normal Operators
by
Toka Diagana
Howard University

We shall study the algebraic sum   S = A + B   , where A and B are unbounded normal operators in a (complex) Hilbert space H. Under appropriate hypotheses, we show that   S    is a normal operator (a question which was open so far). That fact enables us to find conditions for which the unbounded operator,   i S    generates a contraction semigroup. As applications we consider the Cauchy problem given as

ut(x, t) = - i S u(x, t),     +   initial conditions

As illustration, we consider the Schrödinger time-dependent equation with an imaginary mass and complex potential, and the Reaction-Diffusion systems, where the reaction term, F would be zero or linear.

Date received: November 26, 2002