Theory of Commuting Nonselfadjoint Operators Book

Preface. Introduction. I: Operator Vessels in Hilbert Space. 1. Preliminary results. 2. Colligations and vessels. 3. Open systems and open fields. 4. The generalized Cayley-Hamilton theorem. II: Joint Spectrum and Discriminant Varieties of a Commutative Vessel. 5. Joint spectrum and the spectral mapping theorem. 6. Joint spectrum of commuting operators with compact imaginary parts. 7. Properties of discriminant varieties of a commutative vessel. III: Operator Vessels in Banach Spaces. 8. Operator colligations and vessels in Banach space. 9. Bezoutian vessels in Banach space. IV: Spectral Analysis of Two-Operator Vessels. 10. Characteristic functions of two-operator vessels in a Hilbert space. 11. The determinantal representations and the joint characteristic functions in the case of real smooth cubics. 12. Triangular models for commutative two-operator vessels on real smooth cubics. References. Index.