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

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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