Geodesic
Three Test Problems for Quasisimilarity
Canadian journal of mathematics, Tome 39 (1987) no. 4, pp. 880-892

Voir la notice de l'article provenant de la source Cambridge University Press

Kaplansky proposed in [7] three problems with which to test the adequacy of a proposed structure theory of infinite abelian groups. These problems can be rephrased as test problems for a structure theory of operators on Hilbert space. Thus, R. Kadison and I. Singer answered in [6] these test problems for the unitary equivalence of operators. We propose here a study of these problems for quasisimilarity of operators on Hilbert space. We recall first that two (bounded, linear) operators T and T′ acting on the Hilbert spaces and , are said to be quasisimilar if there exist bounded operators and with densely defined inverses, satisfying the relations T′X = XT and TY = YT′. The fact that T and T′ are quasisimilar is indicated by T ∼ T′. The problems mentioned above can now be formulated as follows. 
Bercovici, Hari. Three Test Problems for Quasisimilarity. Canadian journal of mathematics, Tome 39 (1987) no. 4, pp. 880-892. doi: 10.4153/CJM-1987-043-x
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