The present paper deals with the concept of left amenability for a wide range of Banach algebras known as Lau algebras. It gives a fixed point property characterizing left amenable Lau algebras in terms of left Banach -modules. It also offers an application of this result to some Lau algebras related to a locally compact group G, such as the Eymard-Fourier algebra A(G), the Fourier-Stieltjes al...

There is shown that there exists a complete, atomless, σ-centered Boolean algebra, which does not contain any regular countable subalgebra if and only if there exist a nowhere dense ultrafilter. Therefore the existence of such algebras is undecidable in ZFC. A subalgebra B of a Boolean algebra A is called regular whenever for every X ⊆ B, supB X = 1 implies supA X = 1; see e.g. Heindorf and Sha...

We present some connections between the max-min general fuzzy automaton theory and the hyper structure theory. First, we introduce a hyper BCK-algebra induced by a max-min general fuzzy automaton. Then, we study the properties of this hyper BCK-algebra. Particularly, some theorems and results for hyper BCK-algebra are proved. For example, it is shown that this structure consists of different ty...

First we show that the cosets of a fuzzy ideal μ in a BCK-algebraX form another BCK-algebra  X/μ (called the fuzzy quotient BCK-algebra of X by μ). Also we show thatX/μ is a fuzzy partition of X and we prove several some isomorphism theorems. Moreover we prove that if the associated fuzzy similarity relation of a fuzzy partition P of a commutative BCK-algebra iscompatible, then P is a fuzzy quo...

1.1. Probability spaces as von Neumann algebras. The “classical” measure theoretical approach to the study of actions of groups on the probability space is equivalent to a “non-classical” operator algebra approach due to a well known observation of von Neumann, showing that measure preserving isomorphisms between standard probability spaces (X,μ) are in natural correspondence with ∗-algebra iso...

In this note first we define a BCK‐algebra on the states of a deterministic finite automaton. Then we show that it is a BCK‐algebra with condition (S) and also it is a positive implicative BCK‐algebra. Then we find some quotient BCK‐algebras of it. After that we introduce a hyper BCK‐algebra on the set of all equivalence classes of an equivalence relation on the states of a deterministic finite...

1. A finitary probability space (=all probability measures on a fixed finite support) can be faithfully represented by a partial order equipped with a measure of content (e.g. Shannon entropy). 2. This partial order can be obtained via a purely order-theoretic systematic procedure starting from an algebra of properties. This procedure applies to any poset envisioned as an algebra of properties.

Let Ω denote an algebra of sets and μ a σ-finite measure. We then prove that the completion of Ω under the pseudometric d(A,B) = μ∗(A△B) is σ-algebra isomorphic and isometric to the Caratheodory Extension of Ω under the equivalence relation ∼.

We will show that if the cofinality of the ideal of Lebesgue measure zero sets is equal to ω1 then there exists a Boolean algebra B of cardinality ω1 which is not a union of strictly increasing ω-sequence of its subalgebras. This generalizes a result of Just and Koszmider who showed that it is consistent with ZFC+¬CH that such an algebra exists.