About nilpotent C_0-semigroups of operators in the Hilbert spaces and criteria for similarity to the integration operator - Lukashenko, G. V.; Gubreev, G. M. (Methods of Functional Analysis and Topology, 2008)
In the paper, we describe a class of operators A that have empty spectrum and satisfy the nilpotency property of the generated C_0-semigroup U(t)={-iAt}, t0, and such that the operatorA^-1 is similar to the integration operator on the corresponding space L_2(0,a).