In the category of operator spaces, that is, subspaces of the bounded linear operators B(H) on a complex Hilbert space H together with the induced matricial operator norm structure, objects are equivalent if they are completely isometric, i.e., if there is a linear isomorphism between the spaces which preserves this matricial norm structure. Since operator algebras, that is, subalgebras of B(H)...

We define algebras of triple semigroup and DeMorgan triple semigroup and by defining three Mann’s compositions and one unary operation on the set of 3-place(ternary) functions over some set, we construct a DeMorgan triple semigroup of 3-place (ternary) functions and so find an abstract characterization of this algebras.

We study partially and totally associative ternary algebras of first and second kind. Assuming the vector space underlying a ternary algebra to be a topological space and a triple product to be continuous mapping we consider the trivial vector bundle over a ternary algebra and show that a triple product induces a structure of binary algebra in each fiber of this vector bundle. We find the suffi...

Simulation of gate circuits is an efficient method of detecting hazards and oscillations that may occur in the presence of gate and wire delays. Ternary simulation, introduced by Eichelberger in 1965, consists of two algorithms, called A and B, and its results are well understood. Ternary simulation has been generalized by Brzozowski and Ésik in 2003 to an infinite algebra C and finite algebras...

This paper examines ternary algebras, their practical applications and how to translate between the natural dual and the restricted Priestley dual of these algebras. We begin by determining the term functions of the standard ternary algebra as an application of the Baker-Pixley Theorem. This is followed by an overview of some of the practical applications of ternary algebras. We establish the a...

We give a definition and study Hopf structures in ternary ( and n-ary) NambuLie algebra. The fundamental concepts of 3-coalgebra, 3-bialgebra and Hopf 3algebra are introduced. Some examples of Hopf structures are analyzed. Mathematics Subject Classification (1991) 70H99, 58F07 1 [email protected] 2 [email protected] In 1973 Yoishira Nambu [1] proposed a generalization of classical Hamiltonian mecha...