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
On joint distribution in quantum logics. I. Compatible observables
The notion of a joint distribution in -finite measures of observables of a quantum logic defined on some system of -independent Boolean sub--algebras of a Boolean -algebra is studied. In the present first part of the paper the author studies a joint distribution of compatible observables. It is shown that it may exists, although a joint obsevable of compatible observables need not exist.
On joint distribution in quantum logics. II. Noncompatible observables
This paper i a continuation of the first part under the same title. The author studies a joint distribution in -finite measures for noncompatible observables of a quantum logic defined on some system of -independent Boolean sub--algebras of a Boolean -algebra. We present some necessary and sufficient conditions fot the existence of a joint distribution. In particular, it is shown that an arbitrary system of obsevables has a joint distribution in a measure iff it may be embedded into a system...
On joint distributions of observables
On -joint distribution
On mean value in -quantum spaces
The paper deals with a new mathematical model for quantum mechanics based on the fuzzy set theory [1]. The indefinite integral of observables is defined and some basic properties of the integral are examined.
On quantic conuclei in orthomodular lattices.
On representations of logics
On Segal's postulates for general quantum mechanics
On some Feng Qi type -integral inequalities.
On some mappings generating vector -measures
On the cardinality of complex matrix scalings
We disprove a conjecture made by Rajesh Pereira and Joanna Boneng regarding the upper bound on the number of doubly quasi-stochastic scalings of an n × n positive definite matrix. In doing so, we arrive at the true upper bound for 3 × 3 real matrices, and demonstrate that there is no such bound when n ≥ 4.
On the curvature of the space of qubits
The Fisher informational metric is unique in some sense (it is the only Markovian monotone distance) in the classical case. A family of Riemannian metrics is called monotone if its members are decreasing under stochastic mappings. These are the metrics to play the role of Fisher metric in the quantum case. Monotone metrics can be labeled by special operator monotone functions, according to Petz's Classification Theorem. The aim of this paper is to present an idea how one can narrow the set of monotone...
On the factorization criterion for quantum statistics
On the individual ergodic theorem on a logic
On the lattice structure of quantum logics
On the Lebesgue decomposition of a function relative to a -ideal of an orthomodular lattice