Wold-type decompositions and wandering subspaces for operators close to isometries

For operators T satisfying certain inequalities we obtain a weak analog of the classical Wold-Kolmogorov decomposition theorem, representing T as a di rect sum of a unitary operator and a shift operator acting in some Hilbert space of analytic functions. The concept of a dual operator is introduced, which reflects relationships between shift operators acting in two Hilbert spaces of analytic functions dual to each other with respect to the Cauchy pairing. Among different aspects of this duality we consider relationships between hereditary inequalities and properties of reproducing kernels.