Indecomposable operators on Form Hilbert Spaces
Costa A, Tonino
Bull. Belg. Math. Soc. Simon Stevin, Tome 13 (2007) no. 5, p. 811-821 / Harvested from Project Euclid
The class of orthomodular spaces described by Gross and Künzi based on H. Keller's work is a generalization of classic Hilbert spaces. Let $E$ be an orthomodular space in this class, endowed with a positive form $\phi$. As in Hilbert spaces, $\phi$ induces a topology on $E$ making it a complete space. For every $n\in \mathbb{N}$, we describe definite spaces $(E_n,\phi_n)$, with $\dim(E_n)=2^n$ over the base field $K_n=\mathbb{R}((\chi_1,\ldots,\chi_n))$, and we build a family of selfadjoint and indecomposable operators. Later we build an orthomodular definite space $(E,\phi)$ with infinite dimension and we also prove that the sequence of operators in this family induces a bounded, selfadjoint and indecomposable operator in $(E,\phi)$.
Publié le : 2007-12-14
Classification:  Orthomodular spaces,  Hilbert spaces,  46S10,  47B33,  47B38,  54C35
@article{1197908897,
     author = {Costa A, Tonino},
     title = {Indecomposable operators on Form Hilbert Spaces},
     journal = {Bull. Belg. Math. Soc. Simon Stevin},
     volume = {13},
     number = {5},
     year = {2007},
     pages = { 811-821},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1197908897}
}
Costa A, Tonino. Indecomposable operators on Form Hilbert Spaces. Bull. Belg. Math. Soc. Simon Stevin, Tome 13 (2007) no. 5, pp.  811-821. http://gdmltest.u-ga.fr/item/1197908897/