Analytic and Classical Families. Stability.

This chapter focuses attention on the analytic operator families. After studying some universal spectral properties of these families, this chapter deals with the classical families $$ \mathfrak{L}^A $$ of the form 8.1$$ \begin{array}{*{20}c} {\mathfrak{L}^A \left( \lambda \right): = \lambda I_U - A,} & {\lambda \in \mathbb{K}} \\ \end{array} , $$ for a given A ∈$$ A \in \mathcal{L} $$(U), in order to show that, in this particular case, the classic concepts of algebraic ascent and multiplicity equal the generalized concepts introduced in the previous four chapters. Consequently, the algebraic multiplicity analyzed in this book, from a series of different perspectives, is indeed a generalization of the classic concept of algebraic multiplicity. [ABSTRACT FROM AUTHOR]