The Semi-Simplicity Manifold of Arbitrary Operators

Shmuel Kantorovitz
1966 Transactions of the American Mathematical Society  
Introduction. In finite dimensional complex Euclidian space, any linear operator has a unique maximal invariant subspace on which it is semi-simple. It is easily described by means of the Jordan decomposition theorem. The main result of this paper (Theorem 2.1) is a generalization of this fact to infinite dimensional reflexive Banach space, for arbitrary bounded operators T with real spectrum. Our description of the "semi-simplicity manifold" for T is entirely analytic and basis-free, and seems
more » ... therefore to be a quite natural candidate for such generalizations to infinite dimension. A similar generalization to infinite dimension of the concepts of Jordan cells and Weyr characteristic will be presented elsewhere. The theory is motivated and illustrated by examples in §3. Notations. The following notations are fixed throughout this paper, and will be used without further explanation.
doi:10.2307/1994622 fatcat:dp2fkvo5vnedllkip72vb4jgqi