Orthomodular spaces are the counterpart of Hilbert spaces for fields other than or . Both share numerous properties, foremost among them is the validity of the Projection theorem. Nevertheless in the study of bounded linear operators which started in [3], there appeared striking differences with the classical theory. In fact, in this paper we shall construct, on the canonical non-archimedean orthomodular space of [5], two infinite families of self-adjoint bounded linear operators having no invariant closed subspaces other than the trivial ones. Spectrums of such operators contain exactly one point which, therefore, is not an eigenvalue. We also study relations between the subalgebras of bounded linear operators of , which are the commutant of each of these operators, and the algebra studied in [3].
Mots-clés : Indecomposable operators, Algebras of bounded operators
@article{AMBP_2008__15_2_189_0, author = {Barrios Rodr{\'\i}guez, Carla}, title = {Two {Families} of {Self-adjoint} {Indecomposable} {Operators} in an {Orthomodular} {Space}}, journal = {Annales math\'ematiques Blaise Pascal}, pages = {189--209}, publisher = {Annales math\'ematiques Blaise Pascal}, volume = {15}, number = {2}, year = {2008}, doi = {10.5802/ambp.247}, zbl = {1163.47061}, mrnumber = {2473817}, language = {en}, url = {http://www.numdam.org/articles/10.5802/ambp.247/} }
TY - JOUR AU - Barrios Rodríguez, Carla TI - Two Families of Self-adjoint Indecomposable Operators in an Orthomodular Space JO - Annales mathématiques Blaise Pascal PY - 2008 SP - 189 EP - 209 VL - 15 IS - 2 PB - Annales mathématiques Blaise Pascal UR - http://www.numdam.org/articles/10.5802/ambp.247/ DO - 10.5802/ambp.247 LA - en ID - AMBP_2008__15_2_189_0 ER -
%0 Journal Article %A Barrios Rodríguez, Carla %T Two Families of Self-adjoint Indecomposable Operators in an Orthomodular Space %J Annales mathématiques Blaise Pascal %D 2008 %P 189-209 %V 15 %N 2 %I Annales mathématiques Blaise Pascal %U http://www.numdam.org/articles/10.5802/ambp.247/ %R 10.5802/ambp.247 %G en %F AMBP_2008__15_2_189_0
Barrios Rodríguez, Carla. Two Families of Self-adjoint Indecomposable Operators in an Orthomodular Space. Annales mathématiques Blaise Pascal, Tome 15 (2008) no. 2, pp. 189-209. doi : 10.5802/ambp.247. http://www.numdam.org/articles/10.5802/ambp.247/
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