For locally compact groups Gi, i = 1, 2, · · · , n, let CB(G1, · · · , Gn) denote the Banach space of completely bounded multilinear forms on C0(G1)×· · ·×C0(Gn) in the completely bounded norm. CB(G1, · · · , Gn) has the structure of a Banach ∗-algebra under a multiplication and adjoint operation which agree with the convolution structure on the measure algebra M(G1 ×· · ·×Gn). If the Gi are al...

Abstract In this paper a dexterity measure is proposed for driftless nonholonomic systems. Admissible motions at a given state of a nonholonomic system are described by the controllability (Lie) algebra of the system. The algebra is completely described by Lie monomials (vector fields) produced by the Lie bracketing of vector fields associated with the system. At a given state, the nonholonomic...

Then it follows that mvm = m. Our main goal is to find an analogue of the Möbius transform on MV-algebras [4]. To this end, replace the boolean algebra 2X with a semisimple MV-algebra MX . There is no loss of generality in assuming that X is a compact Hausdorff space and MX is a separating MV-algebra of continuous functions over X. Since every Möbius transform mv corresponds to some finitely-ad...

To a given tiling a non commutative space and the corresponding C∗-algebra are constructed. This includes the definition of a topology on the groupoid induced by translations of the tiling. The algebra is also the algebra of observables for discrete models of one or many particle systems on the tiling or its periodic identification. Its scaled ordered K0-group furnishes the gap labelling of Sch...

The present paper deals with the study of the notion of an atom of a function m defined on an effect algebra L with values in [0,∞]; a few examples of atoms for null-additive as well as for non-null-additive functions are also given. We have proved a Saks type decomposition theorem for an element a with m(a) > 0 (for a suitable m), which does not contain any atom of m, in a σ-complete effect al...

In this paper we continue development of formal theory of a special class offuzzy logics, called EQ-logics. Unlike fuzzy logics being extensions of theMTL-logic in which the basic connective is implication, the basic connective inEQ-logics is equivalence. Therefore, a new algebra of truth values calledEQ-algebra was developed. This is a lower semilattice with top element endowed with two binary...

We present the material in a slightly different order than it is usually done (such as e.g. in the course book). Here we prefer to start out with an abelian C∗-algebra A (say, the algebra C∗(a) generated by a normal operator a ∈ B(H)) and construct from it the spectral measure. This is done as follows: We know that A is isomorphic to C(X), the algebra of continuous functions on a compact set X....

We consider smooth actions of lattices in higher-rank semisimple Lie groups on manifolds. define two numbers $r(G)$ and $m(G)$ associated with the roots system algebra a group $G$. If dimension manifold is smaller than $r(G)$, then we show action preserves Borel probability measure. at most $m(G)$, there quasi-invariant measure such that measurably isomorphic to relatively measure-preserving ov...

We prove that every closed exhaustive vector-valued modular measure on a lattice ordered effect algebra L can be decomposed into the sum of a Lyapunov exhaustive modular measure (i.e. its restriction to every interval of L has convex range) and an ”antiLyapunov” exhaustive modular measure. This result extends a Kluvanek-Knowles decomposition theorem for measures on Boolean algebras.

In this paper, first we define the notion of involutive operator on bounded involutive equality algebras and by using it, we introduce a new class of equality algebras that we called it a tense like equality algebra. Then we investigate some properties of tense like equality algebra. For two involutive bounded equality algebras and an equality homomorphism between them, we prove that the tense ...