Chapter 8: Triangular Representations of Non-selfadjoint Operators

The present chapter deals with non-compact non-normal operators A in a separable Hilbert space ℋ. Besides, it is supposed that either A*–A ∈ SN_p or A*A–I ∈ SN_p (p ≥ 1). We suggest the triangular representations of the considered operators via chains of their invariant projections. These representations are our main tool in the next two chapters devoted to operator functions of non-selfadjoint operators and the relevant operator equations.

All the operators considered in this chapter are bounded operators in ℋ.