Geodesic
Generators of Nest Algebras
Canadian journal of mathematics, Tome 26 (1974) no. 3, pp. 565-575

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

A collection of subspaces of a Hilbert space is called a nest if it is totally ordered by inclusion. The set of all bounded linear operators leaving invariant each member of a given nest forms a weakly-closed algebra, called a nest algebra. Nest algebras were introduced by J. R. Ringrose in [9]. The present paper is concerned with generating nest algebras as weakly-closed algebras, and in particular with the following question which was first raised by H. Radjavi and P. Rosenthal in [8], viz: Is every nest algebra on a separable Hilbert space generated, as a weakly-closed algebra, by two operators? That the answer to this question is affirmative is proved by first reducing the problem using the main result of [8] and then by using a characterization of nests due to J. A. Erdos [2]. 
Longstaff, W. E. Generators of Nest Algebras. Canadian journal of mathematics, Tome 26 (1974) no. 3, pp. 565-575. doi: 10.4153/CJM-1974-052-8
@article{10_4153_CJM_1974_052_8,
     author = {Longstaff, W. E.},
     title = {Generators of {Nest} {Algebras}},
     journal = {Canadian journal of mathematics},
     pages = {565--575},
     year = {1974},
     volume = {26},
     number = {3},
     doi = {10.4153/CJM-1974-052-8},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1974-052-8/}
}
TY  - JOUR
AU  - Longstaff, W. E.
TI  - Generators of Nest Algebras
JO  - Canadian journal of mathematics
PY  - 1974
SP  - 565
EP  - 575
VL  - 26
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1974-052-8/
DO  - 10.4153/CJM-1974-052-8
ID  - 10_4153_CJM_1974_052_8
ER  - 
%0 Journal Article
%A Longstaff, W. E.
%T Generators of Nest Algebras
%J Canadian journal of mathematics
%D 1974
%P 565-575
%V 26
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1974-052-8/
%R 10.4153/CJM-1974-052-8
%F 10_4153_CJM_1974_052_8

[1] 1. Dixmier, J., Les algèbres d'opérateurs dans l'espace Hilbertien (Gauthier-Villars, Paris, 1957). Google Scholar

[2] 2. Erdos, J. A., On some non-s elf-adjoint algebras of operators, Ph.D. Thesis, Peterhouse College, Cambridge 1964. Google Scholar

[3] 3. Erdos, J. A., Unitary invariants for nests, Pacific J. Math. 23 (1967), 229–256. Google Scholar

[4] 4. Halmos, P. R., Measure theory (Van Nostrand, Princeton, 1955). Google Scholar

[5] 5. Kadison, R. V. and Singer, I. M., Triangular operator algebras, Amer. J. Math. 82 (1960), 227–259. Google Scholar

[6] 6. Kelley, J. L., General topology (Van Nostrand, Princeton, 1955). Google Scholar

[7] 7. von Neumann, J., Zür Algebra der Funktionaloperationen und Théorie der Normalen Operatoren, Math. Ann. 102 (1929), 370–427. Google Scholar

[8] 8. Radjavi, H. and Rosenthal, P., On invariant subspaces and reflexive algebras, Amer. J. Math. 91 (1969), 683–692. Google Scholar

[9] 9. Ringrose, J. R., On some algebras of operators, Proc. London Math. Soc. 15 (1965), 61–83. Google Scholar

[10] 10. Rosenthal, P., Completely reducible operators, Proc. Amer. Math. Soc. 19 (1968), 826–830. Google Scholar

Cité par Sources :