# Addendum to: "Infinite-dimensional versions of the primary, cyclic and Jordan decompositions", by M. Radjabalipour

Authors

1 University of New Hampshire

2 College of Engineering and Physical Sciences, University of New Hampshire, Durham, USA.

Abstract

In his paper mentioned in the title, which appears in the same issue of this journal, Mehdi Radjabalipour derives the cyclic decomposition of an algebraic linear transformation. A more general structure theory for linear transformations appears in Irving Kaplansky's lovely 1954 book on infinite abelian groups. We present a translation of Kaplansky's results for abelian groups into the terminology of linear transformations. We add an additional translation of a ring-theoretic result to give a characterization of algebraically hyporeflexive transformations and the strict closure of the set of polynomials in a transformation $T$.

Keywords

Main Subjects

### History

• Receive Date: 23 May 2015
• Revise Date: 04 July 2015
• Accept Date: 04 July 2015