Geodesic
Subnormality and generalized commutation relations of families of operators†
Glasgow mathematical journal, Tome 32 (1990) no. 2, pp. 231-238

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

1. Every family of subnormal operators in a Hilbert space fulfils the Halmos-Bram condition on a suitable dense subset of its domain [2], [3]. In [2] and [4] it is shown that the generalized commutation relation implies the Halmos-Bram condition for one operator. In this paper it is proved that the generalized commutation relation implies the Halmos-Bram condition for infinite families of operators (in a special case Jorgensen proved it in a different way for finite families of operators, see [2]) and as an example of the application of this property it is shown that every family of generalized creation operators in the Bargmann space of an infinite order, indexed by mutually orthogonal vectors from I2 is subnormal. See [1] for the definitions. 
Stochel, Jerzy Bartłomiej. Subnormality and generalized commutation relations of families of operators†. Glasgow mathematical journal, Tome 32 (1990) no. 2, pp. 231-238. doi: 10.1017/S0017089500009277
@article{10_1017_S0017089500009277,
     author = {Stochel, Jerzy Bart{\l}omiej},
     title = {Subnormality and generalized commutation relations of families of operators{\textdagger}},
     journal = {Glasgow mathematical journal},
     pages = {231--238},
     year = {1990},
     volume = {32},
     number = {2},
     doi = {10.1017/S0017089500009277},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089500009277/}
}
TY  - JOUR
AU  - Stochel, Jerzy Bartłomiej
TI  - Subnormality and generalized commutation relations of families of operators†
JO  - Glasgow mathematical journal
PY  - 1990
SP  - 231
EP  - 238
VL  - 32
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.1017/S0017089500009277/
DO  - 10.1017/S0017089500009277
ID  - 10_1017_S0017089500009277
ER  - 
%0 Journal Article
%A Stochel, Jerzy Bartłomiej
%T Subnormality and generalized commutation relations of families of operators†
%J Glasgow mathematical journal
%D 1990
%P 231-238
%V 32
%N 2
%U http://geodesic.mathdoc.fr/articles/10.1017/S0017089500009277/
%R 10.1017/S0017089500009277
%F 10_1017_S0017089500009277

[1] 1.Bargmann, V., Remarks on a Hilbert space of analytic functions, Proc. Nat. Acad. Sci. U.S.A. 48 (1962), 199–204. Google Scholar PubMed | DOI

[2] 2.Jorgensen, P. T. E., Commutative algebras of unbounded operators, Math. Anal. Appl. 123 (1987), 508–527. Google Scholar | DOI

[3] 3.Stochel, J. and Szafraniec, F. H., On normal extensions of unbounded operators I J. Operator Theory 14 (1985), 31–55. Google Scholar

[4] 4.Stochel, J. B., Subnormality and generalized commutation relations, Glasgow Math. J. 30 (1988), 259–262. Google Scholar | DOI

[5] 5.Stochel, J. B., Subnormality of generalized creation operators in Bargmann's Hilbert space of an infinite order, in preparation. Google Scholar

Cité par Sources :