Geodesic
A Purity Criterion for Pairs of Linear Transformations
Canadian journal of mathematics, Tome 26 (1974) no. 3, pp. 734-745

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

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:X → Y (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 C 2-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 
Fixman, Uri; Zorzitto, Frank A. A Purity Criterion for Pairs of Linear Transformations. Canadian journal of mathematics, Tome 26 (1974) no. 3, pp. 734-745. doi: 10.4153/CJM-1974-068-8
@article{10_4153_CJM_1974_068_8,
     author = {Fixman, Uri and Zorzitto, Frank A.},
     title = {A {Purity} {Criterion} for {Pairs} of {Linear} {Transformations}},
     journal = {Canadian journal of mathematics},
     pages = {734--745},
     year = {1974},
     volume = {26},
     number = {3},
     doi = {10.4153/CJM-1974-068-8},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1974-068-8/}
}
TY  - JOUR
AU  - Fixman, Uri
AU  - Zorzitto, Frank A.
TI  - A Purity Criterion for Pairs of Linear Transformations
JO  - Canadian journal of mathematics
PY  - 1974
SP  - 734
EP  - 745
VL  - 26
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1974-068-8/
DO  - 10.4153/CJM-1974-068-8
ID  - 10_4153_CJM_1974_068_8
ER  - 
%0 Journal Article
%A Fixman, Uri
%A Zorzitto, Frank A.
%T A Purity Criterion for Pairs of Linear Transformations
%J Canadian journal of mathematics
%D 1974
%P 734-745
%V 26
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1974-068-8/
%R 10.4153/CJM-1974-068-8
%F 10_4153_CJM_1974_068_8

[1] 1. Aronszajn, N., Quadratic forms on vector spaces, Proc. Intern. Symposium on Linear Spaces 1960, Jerusalem, 1961. Google Scholar

[2] 2. Aronszajn, N. and Brown, R. D., Finite-dimensional perturbaions of spectral problems and variational approximation methods for eigenvalue problems. I: Finite-dimensional perturbations, Studia Math. 36 (1970), 1–76. Google Scholar

[3] 3. Aronszajn, N. and Fixman, U., Algebraic spectral problems, Studia Math. 30 (1968), 273–338. Google Scholar

[4] 4. Dickson, S. E., A torsion theory for abelian categories, Trans. Amer. Math. Soc. 121 (1966), 223–235. Google Scholar

[5] 5. Fixman, U., On algebraic equivalence between pairs of linear transformations, Trans. Amer. Math. Soc. 113 (1964), 424–453. Google Scholar

[6] 6. Zorzitto, F. A., Topological decompositions in systems of linear transformations, Ph.D. Thesis, Queen's University, 1972. Google Scholar

[7] 7. Zorzitto, F. A., Purity and copurity in systems of linear transformations (to appear). Google Scholar

Cité par Sources :