Open Access
December 2007 Indecomposable operators on Form Hilbert Spaces
Tonino Costa A
Bull. Belg. Math. Soc. Simon Stevin 14(5): 811-821 (December 2007). DOI: 10.36045/bbms/1197908897


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 $(E,\phi)$.


Download Citation

Tonino Costa A. "Indecomposable operators on Form Hilbert Spaces." Bull. Belg. Math. Soc. Simon Stevin 14 (5) 811 - 821, December 2007.


Published: December 2007
First available in Project Euclid: 17 December 2007

zbMATH: 1135.46043
MathSciNet: MR2378991
Digital Object Identifier: 10.36045/bbms/1197908897

Primary: ‎46S10
Secondary: 47B33 , 47B38 , 54C35‎

Keywords: ‎Hilbert spaces , Orthomodular spaces

Rights: Copyright © 2007 The Belgian Mathematical Society

Vol.14 • No. 5 • December 2007
Back to Top