On Bilinear Forms from the Point of View of Generalized Effect Algebras

Warning

This publication doesn't include Faculty of Arts. It includes Faculty of Science. Official publication website can be found on muni.cz.

Authors	DVUREČENSKIJ Anatolij JANDA Jiří
Year of publication	2013
Type	Article in Periodical
Magazine / Source	Foundations of Physics
MU Faculty or unit	Faculty of Science
Citation
Web	http://link.springer.com/article/10.1007%2Fs10701-013-9736-2
Doi	http://dx.doi.org/10.1007/s10701-013-9736-2
Field	General mathematics
Keywords	Effect algebra; generalized effect algebra; Hilbert space; operator; unbounded operator; bilinear form; singular bilinear form; regular bilinear form; monotone convergence
Description	We study positive bilinear forms on a Hilbert space which are neither not necessarily bounded nor induced by some positive operator. We show when different families of bilinear forms can be described as a generalized effect algebra. In addition, we present families which are or are not monotone downwards (Dedekind upwards) $\sigma$-complete generalized effect algebras.
Related projects:	Mathematical structures and their physical applications