Geodesic
THE STATE-SPACE OF THE LATTICE OF ORTHOGONALLY CLOSED SUBSPACES
Glasgow mathematical journal, Tome 47 (2005) no. 1, pp. 213-220

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

DOI

The notion of a strongly dense inner product space is introduced and it is shown that, for such an incomplete space $S$ (in particular, for each incomplete hyperplane of a Hilbert space), the system $F(S)$ of all orthogonally closed subspaces of $S$ is not stateless, and the state-space of $F(S)$ is affinely homeomorphic to the face consisting of the free states on the projection lattice corresponding to the completion of $S$. The homeomorphism is determined by the extension of the states. In particular, when $S$ is complex, the state-space of $F(S)$ is affinely homeomorphic to the state-space of the Calkin algebra associated with $\skew3\overline S$.
DOI : 10.1017/S0017089504002174
Mots-clés : Primary 46C05, 46L30, Secondary 03G12 
CHETCUTI, E.; DVUREČENSKIJ, A. THE STATE-SPACE OF THE LATTICE OF ORTHOGONALLY CLOSED SUBSPACES. Glasgow mathematical journal, Tome 47 (2005) no. 1, pp. 213-220. doi: 10.1017/S0017089504002174
@article{10_1017_S0017089504002174,
     author = {CHETCUTI, E. and DVURE\v{C}ENSKIJ, A.},
     title = {THE {STATE-SPACE} {OF} {THE} {LATTICE} {OF} {ORTHOGONALLY} {CLOSED} {SUBSPACES}},
     journal = {Glasgow mathematical journal},
     pages = {213--220},
     year = {2005},
     volume = {47},
     number = {1},
     doi = {10.1017/S0017089504002174},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089504002174/}
}
TY  - JOUR
AU  - CHETCUTI, E.
AU  - DVUREČENSKIJ, A.
TI  - THE STATE-SPACE OF THE LATTICE OF ORTHOGONALLY CLOSED SUBSPACES
JO  - Glasgow mathematical journal
PY  - 2005
SP  - 213
EP  - 220
VL  - 47
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.1017/S0017089504002174/
DO  - 10.1017/S0017089504002174
ID  - 10_1017_S0017089504002174
ER  - 
%0 Journal Article
%A CHETCUTI, E.
%A DVUREČENSKIJ, A.
%T THE STATE-SPACE OF THE LATTICE OF ORTHOGONALLY CLOSED SUBSPACES
%J Glasgow mathematical journal
%D 2005
%P 213-220
%V 47
%N 1
%U http://geodesic.mathdoc.fr/articles/10.1017/S0017089504002174/
%R 10.1017/S0017089504002174
%F 10_1017_S0017089504002174

Cité par Sources :