Logics with separating sets of measures
Mac Neille completion of centers and centers of Mac Neille completions of lattice effect algebras
If element of a lattice effect algebra is central, then the interval is a lattice effect algebra with the new top element and with inherited partial binary operation . It is a known fact that if the set of central elements of is an atomic Boolean algebra and the supremum of all atoms of in equals to the top element of , then is isomorphic to a subdirect product of irreducible effect algebras ([18]). This means that if there exists a MacNeille completion of which is its extension...
Matrix representation of finite effect algebras
In this paper we present representation of finite effect algebras by matrices. For each non-trivial finite effect algebra we construct set of matrices in such a way that effect algebras and are isomorphic if and only if . The paper also contains the full list of matrices representing all nontrivial finite effect algebras of cardinality at most .
Measures on orthomodular vector space lattices
Minimal and maximal sets of Bell-type inequalities holding in a logic.
Modular atomic effect algebras and the existence of subadditive states
Lattice effect algebras generalize orthomodular lattices and -algebras. We describe all complete modular atomic effect algebras. This allows us to prove the existence of ordercontinuous subadditive states (probabilities) on them. For the separable noncomplete ones we show that the existence of a faithful probability is equivalent to the condition that their MacNeille complete modular effect algebra.
Modularity, atomicity and states in Archimedean lattice effect algebras.
Morphisms and pasting of orthoalgebras
New operations on partial Abelian monoids defined by preideals
We consider partial abelian monoids, in particular generalized effect algebras. From the given structures, we construct new ones by introducing a new operation , which is given by restriction of the original partial operation + with respect to a special subset called preideal. We bring some derived properties and characterizations of these new built structures, supporting the results by illustrative examples.
Nonatomic states
Note on a construction of unbounded measures on a nonseparable Hilbert space quantum logic
Observables on -MV algebras and -lattice effect algebras
Effect algebras were introduced as abstract models of the set of quantum effects which represent sharp and unsharp properties of physical systems and play a basic role in the foundations of quantum mechanics. In the present paper, observables on lattice ordered -effect algebras and their “smearings” with respect to (weak) Markov kernels are studied. It is shown that the range of any observable is contained in a block, which is a -MV algebra, and every observable is defined by a smearing of a sharp...
On a summability of observables in generalized measurable spaces
On centers and state spaces of logics
On complete-cocomplete subspaces of an inner product space
In this note we give a measure-theoretic criterion for the completeness of an inner product space. We show that an inner product space is complete if and only if there exists a -additive state on , the orthomodular poset of complete-cocomplete subspaces of . We then consider the problem of whether every state on , the class of splitting subspaces of , can be extended to a Hilbertian state on ; we show that for the dense hyperplane (of a separable Hilbert space) constructed by P. Pták and...
On direct decompositions of certain orthomodular lattices.
On extension properties for observables
On generating and concreteness in quantum logics
On interval homogeneous orthomodular lattices
An orthomodular lattice is said to be interval homogeneous (resp. centrally interval homogeneous) if it is -complete and satisfies the following property: Whenever is isomorphic to an interval, , in then is isomorphic to each interval with and (resp. the same condition as above only under the assumption that all elements , , , are central in ). Let us denote by Inthom (resp. Inthom) the class of all interval homogeneous orthomodular lattices (resp. centrally interval homogeneous...
On isomorphisms of inner product spaces