Positive projections as generators of $J$-projections of type~(B)
Lobachevskii journal of mathematics, Tome 26 (2007), pp. 91-105.

Voir la notice de l'article provenant de la source Math-Net.Ru

Let $\mathcal A$ be a von Neumann $J$-algebra of type (B) acting in an indefinite metric space. The aim of the paper is to study $J$-projections from $\mathcal A$.
Keywords: quantum logic, Hilbert space, indefinite metric space, projection.
@article{LJM_2007_26_a9,
     author = {M. S. Matveichuk and A. M. Ionova},
     title = {Positive projections as generators of $J$-projections of {type~(B)}},
     journal = {Lobachevskii journal of mathematics},
     pages = {91--105},
     publisher = {mathdoc},
     volume = {26},
     year = {2007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/LJM_2007_26_a9/}
}
TY  - JOUR
AU  - M. S. Matveichuk
AU  - A. M. Ionova
TI  - Positive projections as generators of $J$-projections of type~(B)
JO  - Lobachevskii journal of mathematics
PY  - 2007
SP  - 91
EP  - 105
VL  - 26
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/LJM_2007_26_a9/
LA  - en
ID  - LJM_2007_26_a9
ER  - 
%0 Journal Article
%A M. S. Matveichuk
%A A. M. Ionova
%T Positive projections as generators of $J$-projections of type~(B)
%J Lobachevskii journal of mathematics
%D 2007
%P 91-105
%V 26
%I mathdoc
%U http://geodesic.mathdoc.fr/item/LJM_2007_26_a9/
%G en
%F LJM_2007_26_a9
M. S. Matveichuk; A. M. Ionova. Positive projections as generators of $J$-projections of type~(B). Lobachevskii journal of mathematics, Tome 26 (2007), pp. 91-105. http://geodesic.mathdoc.fr/item/LJM_2007_26_a9/

[1] Birkhoff G., Lattice Theory, Providence, Rhode Island, 1967 | MR

[2] Linear operators in space with an indefinite metric, Wiley, New York, 1989 | MR | Zbl

[3] Theoretical and Mathematical Physics, 54 (1983), 35–48 | DOI | MR | Zbl | Zbl

[4] Functional analysis and its applications, 13:4 (1979), 305–307 | DOI | MR

[5] Matvejchuk M. S., “Probability measures in $W^*J$-algebras in Hilbert spaces with conjugation”, Proc. Amer. Math. Soc., 126:4 (1998), 1155–1164 | DOI | MR | Zbl

[6] Matvejchuk M. S. and Ionova A. M., “The structure of $J$-projections from logics of type $(B)$”, 8th Bienuial IQSA Meeting Quantum Structures 06, Abstracts (Malta, 2006, July, 9–14), 62–63

[7] Sov. Math. Dokl., 44:1 (1992), 161–165 | MR | Zbl