Geodesic
Compact Perturbations of Reflexive Algebras
Canadian journal of mathematics, Tome 33 (1981) no. 3, pp. 685-700

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

In this paper we study lattice properties of operator algebras which are invariant under compact perturbations. It is easy to see that if and are two operator algebras with contained in , then the reverse inclusion holds for their lattices of invariant subspaces. We will show that in certain cases, the assumption thats is contained in , where is the ideal of compact operators, implies that the lattice of is “approximately” contained in the lattice of . In particular, supposed and are reflexive and have commutative subspace lattices containing “enough” finite dimensional elements. We show (Corollary 2.8) that if is unitarily equivalent to a subalgebra of , then there is a unitary operator which carries all “sufficiently large” subspaces in lat into lat . 
Davidson, Kenneth R. Compact Perturbations of Reflexive Algebras. Canadian journal of mathematics, Tome 33 (1981) no. 3, pp. 685-700. doi: 10.4153/CJM-1981-054-0
@article{10_4153_CJM_1981_054_0,
     author = {Davidson, Kenneth R.},
     title = {Compact {Perturbations} of {Reflexive} {Algebras}},
     journal = {Canadian journal of mathematics},
     pages = {685--700},
     year = {1981},
     volume = {33},
     number = {3},
     doi = {10.4153/CJM-1981-054-0},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1981-054-0/}
}
TY  - JOUR
AU  - Davidson, Kenneth R.
TI  - Compact Perturbations of Reflexive Algebras
JO  - Canadian journal of mathematics
PY  - 1981
SP  - 685
EP  - 700
VL  - 33
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1981-054-0/
DO  - 10.4153/CJM-1981-054-0
ID  - 10_4153_CJM_1981_054_0
ER  - 
%0 Journal Article
%A Davidson, Kenneth R.
%T Compact Perturbations of Reflexive Algebras
%J Canadian journal of mathematics
%D 1981
%P 685-700
%V 33
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1981-054-0/
%R 10.4153/CJM-1981-054-0
%F 10_4153_CJM_1981_054_0

[1] 1. Arveson, W. B., Interpolation in nest algebras, J. Func. Anal. 20 (1972), 208–233. Google Scholar

[2] 2. Davidson, K. R., Commutative subspace lattices, Indiana Univ. Math. J. 27, 479–490. Google Scholar

[3] 3. Davidson, K. R. and Fong, C. K., An operator algebra which is not closed in the Calkin algebra, Pac. J. Math. 72, 57–58. Google Scholar

[4] 4. Fall, T., Arveson, W. and Muhly, P., Perturbations of nest algebras, J. Oper. Th. 1. Google Scholar

[5] 5. Halmos, P. R., Quasitriangular operators, Acta Sci. Math. (Szeged) 29 (1968), 283–293. Google Scholar

[6] 6. Hopenwasser, A. and Plastiras, J., Isometries of quasitriangular operator algebras, to appear. Google Scholar

[7] 7. Johnson, B. E. and Parrot, S. K., Operators commuting with a von Neumann Algebra modulo the set of compact operators, J. Func. Anal. 11 (1972), 39–61. Google Scholar

[8] 8. Plastiras, J., Quasitriangular operator algebras, Pac. J. Math. 64 (1976), 543–549. Google Scholar

[9] 9. Plastiras, J., Compact perturbations of certain von Neumann algebras, Trans. AMS 234 (1977), 561–577. Google Scholar

Cité par Sources :