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.
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