Wyniki wyszukiwania - BazTech

1

Completeness of Inner Product Spaces and G. Cattaneo

Buhagiar D., Chetcuti E., Dvurečenskij A.

Fundamenta Informaticae

|

2012

|

Vol. 115, nr 1

15-24

EN

In the Eighties G. Cattaneo contributed to Hilbert space quantummechanicsmodels using the family of splitting subspaces of an inner product space in order to find completeness criteria. In this paper we show how that theory was developed in the last 25 years into a rich theory which has a close connection to quantum information. G. Cattaneo also posed an open problem which was solved only this year.

2

Measure-theoretic characterizations of certain topological properties

Buhagiar D., Chetcuti E., Dvurečenskij A.

Bulletin of the Polish Academy of Sciences. Mathematics

|

2005

|

Vol. 53, no 1

99-109

EN

It is shown that Cech completeness, ultracompleteness and local compactness can be denned by demanding that certain equivalences hold between certain classes of Baire measures or by demanding that certain classes of Baire measures have non-empty support. This shows that these three topological properties are measurable, similarly to the classical examples of compact spaces, pseudo-compact spaces and realcompact spaces.

3

On pseudo-effect algebras which can be covered by pseudo MV-algebras

Dvurečenskij A., Vetterlein T.

Demonstratio Mathematica

|

2003

|

Vol. 36, nr 2

261--282

EN

Pseudo-effect algebras are partial algebras (E; +, 0,1) which were recently introduced. They have a partially defined addition + which is only associative and not necessary commutative and with two complements, left and right ones. They are a non-commutative generalization of orthomodular posets and MV-algebras, respectively. We define five kinds of compatibilities, and we introduce a block as a maximal set of mutually compatible elements. The compatibility is a property of the physical system which corresponds to the distributivity, or equivalently, to "classical mechanics"-type phenomena. We show that any lattice pseudo-effect algebra under a natural condition can be covered by blocks, and any block is a pseudo MV-algebra. This result generalizes the analogical result of Riecanova for effect algebras. If the pseudo-effect algebra with the condition is, in addition, a (7-complete lattice, then it is a commutative effect algebra which can be covered by cr-complete MV-algebras.

4

Test spaces, pseudo-effect algebras, and tensor product of pseudo-effect algebras

Dvurečenskij A.

Demonstratio Mathematica

|

2002

|

Vol. 35, nr 4

699-715

EN

Inspiring the ideas of the test spaces of effect algebras, we introduce test spaces of pseudo-effect algebras. We show that there is a one-to-one correspondence among algebraic test spaces and pseudo-effect algebras. This correspondence gives a test on a pseudo-effect algebra as a decomposition of unity, which corresponds to hypothesis in the statistical models. This correspondence allows us to define a tensor product of pseudo-effect algebras as well as bounded Boolean power. In addition, we introduce PMV-test spaces which forces pseudo MV-algebras.

5

Meanders in orthoposets and QMV algebras

Dvurečenskij A., Pulmannova S., Salvati S.

Demonstratio Mathematica

|

2001

|

Vol. 34, nr 1

1-11

EN

The notion of a meander of an ideal in lattices is generalized in two directions: to ideals in orthoposets and to ideals in QMV-algebras, and used to a characterization of subclasses of the above structures, namely Boolean orthoposets and QMV-algebras m which every ideal is closed under perspectivity, and to a characterization of Riesz ideals in orthoposets and perspectivity closed ideals in QMV algebras.