Geodesic
On the Structure of Certain Nest Algebra Modules
Canadian journal of mathematics, Tome 39 (1987) no. 6, pp. 1405-1412

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

Let be a nest algebra of operators on some Hilbert space H. Weakly closed -modules were first studied by J. Erdos and S. Power in [4]. It became apparent that many interesting classes of non self-adjoint operator algebras arise as just such a module. This paper undertakes a systematic investigation of the correspondence which arises between such modules and order homomorphisms from Lat into itself. This perspective provides a basis to answer some open questions arising from [4]. In particular, the questions concerning unique “determination” and characterization of maximal and minimal elements under this correspondence, are resolved. This is then used to establish when the determining homomorphism is unique. 
Knowles, G. J. On the Structure of Certain Nest Algebra Modules. Canadian journal of mathematics, Tome 39 (1987) no. 6, pp. 1405-1412. doi: 10.4153/CJM-1987-065-7
@article{10_4153_CJM_1987_065_7,
     author = {Knowles, G. J.},
     title = {On the {Structure} of {Certain} {Nest} {Algebra} {Modules}},
     journal = {Canadian journal of mathematics},
     pages = {1405--1412},
     year = {1987},
     volume = {39},
     number = {6},
     doi = {10.4153/CJM-1987-065-7},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1987-065-7/}
}
TY  - JOUR
AU  - Knowles, G. J.
TI  - On the Structure of Certain Nest Algebra Modules
JO  - Canadian journal of mathematics
PY  - 1987
SP  - 1405
EP  - 1412
VL  - 39
IS  - 6
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1987-065-7/
DO  - 10.4153/CJM-1987-065-7
ID  - 10_4153_CJM_1987_065_7
ER  - 
%0 Journal Article
%A Knowles, G. J.
%T On the Structure of Certain Nest Algebra Modules
%J Canadian journal of mathematics
%D 1987
%P 1405-1412
%V 39
%N 6
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1987-065-7/
%R 10.4153/CJM-1987-065-7
%F 10_4153_CJM_1987_065_7

[1] 1. Knowles, G. J., Dissertation, Kings College (University of London, 1981). Google Scholar

[2] 2. Knowles, G. J., Nest algebra-modules; commutants and cohomology, (Submitted). Google Scholar

[3] 3. Erdos, J. A., Operators of finite rank in nest algebras, J. London Math. Soc. 43 (1968), 391–397. Google Scholar

[4] 4. Erdos, J. A. and Power, S. C., Weakly closed ideals of nest algebras, J. Op. Theory 7 (1982), 219–235. Google Scholar

[5] 5. Ringrose, J. R., On some algebras of operators, Proc. London Math. Soc. (3) 15 (1965), 61–83. Google Scholar

Cité par Sources :