The joint characteristic function of a commutative operator vessel in Banach space
The characteristic function of a single operator, a basic object of study in modern operator theory, was generalized by M. S. Livsic to a class of pairs of commuting linear operators. There exists at present a well developed theory of joint characteristic functions, with application to operator theory, algebraic geometry and systems theory, see \textit{N. Kravitsky}, \textit{M. S. Livsic}, \textit{A. Markus} and \textit{V. Vinnikov}, ``Theory of commuting non-selfadjoint operators'' (1995; Zbl 0834.47004). The paper deals with \(n\)-tuples of commuting operators in Banach space, with \(n>2\). The programme of regarding the joint characteristic function as a morphism of vector bundles, carried by the discriminant variety of the system is developed in analogy with the known case of commuting pairs of operators.
scientific article; zbMATH DE number 908005