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A Purity Criterion for Pairs of Linear Transformations

Published online by Cambridge University Press:  20 November 2018

Uri Fixman
Affiliation:
Queen's University, Kingston, Ontario
Frank A. Zorzitto
Affiliation:
Queen's University, Kingston, Ontario
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In connection with the study of perturbation methods for differential eigenvalue problems, Aronszajn put forth a theory of systems (X, Y; A, B) consisting of a pair of linear transformations A, B:XY (see [1]; cf. also [2]). Here X and Y are complex vector spaces, possibly of infinite dimension. The algebraic aspects of this theory, where no restrictions of topological nature are imposed, where developed in [3] and [5]. We hasten to point out that the category of C2-systems (definition in § 1) in which this algebraic investigation takes place is equivalent to the category of all right modules over the ring of matrices of the form

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1974

References

1. Aronszajn, N., Quadratic forms on vector spaces, Proc. Intern. Symposium on Linear Spaces 1960, Jerusalem, 1961.Google Scholar
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7. Zorzitto, F. A., Purity and copurity in systems of linear transformations (to appear).Google Scholar