The Three Test Problems of Kaplansky for Hilbert C*-modules
by
Bola O. Balogun
Mathematics & cOmputer Science Department, National University of Lesotho, P.O.Roma 180, Lesotho, Southern Africa.

In his tract on infinite abelian groups, I. Kaplansky suggests three problems with which to test the adequacy of a purported structure theory for the subject. The problems, being general, are of interest by themselves. He notes that they provide a worthy test in other subjects. In particular, Kaplansky has suggested these problems, suitably rephrased, as a test of a unitary equivalence theory for operators on a Hilbert space. This has been taken up by various authors. In this paer we study these problems in the context of unitary equivalence of Hilbert C*-modules operators.

Date received: May 25, 2002