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

Authors

  • D. Hadwin 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 $T$.

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Journal title

volume 41  issue Issue 7 (Special Issue)

pages  155- 173

publication date 2015-12-01

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