In this paper, we introduce a notion of generalized states from an EQ-algebra E1 to another EQ-algebra E2, which is a generalization of internal states (or state operators) on an EQ-algebra E. Also we give a type of special generalized state from an EQ-algebra E1 to E1, called generalized internal states (or GI-state). Then we give some examples and basic properties of generalized (internal) st...

A C *-algebra A is called an ideal C * -algebra (or equally a dual algebra) if it is an ideal in its bidual A**. M.C.F. Berglund proved that subalgebras and quotients of ideal C*-algebras are also ideal C*-algebras, that a commutative C *-algebra A is an ideal C *-algebra if and only if it is isomorphicto C (Q) for some discrete space ?. We investigate ideal J*-algebras and show that the a...

We introduce a notion of secondary characteristic classes of Lie algebra extensions. As a spin-off of our construction we obtain a new proof of Lecomte’s generalization of the Chern–Weil homomorphism.

let $a$ be a banach algebra and $x$ be a banach $a$-bimodule. then ${mathcal{s}}=a oplus x$, the $l^1$-direct sum of $a$ and $x$ becomes a module extension banach algebra when equipped with the algebra product $(a,x).(a',x')=(aa',ax'+xa').$ in this paper, we investigate biflatness and biprojectivity for these banach algebras. we also discuss on automatic continuity of derivations on ${mathcal{s...

We define the Lukasiewicz transform as a residuated map and a homomorphism between semimodules over the semiring reducts of an MV-algebra. Then we describe the “ Lukasiewicz Transform Based” ( LTB) algorithm for image processing, demonstrating its applicability.

Abstract Let G be a group and A set equipped with collection of finitary operations. We study cellular automata $$\tau :{A^G} \to {A^G}$$ that preserve the operations induced componentwise from . show τ is an endomorphism if only its local function homomorphism. When entropic (i.e. all are homomorphisms), we establish EndCA( G;A ), consisting such endomorphic automata, isomorphic to direct limi...

Abstract. Let K be any unital commutative Q-algebra and z = (z1, z2, · · · , zn) commutative or noncommutative variables. Let t be a formal central parameter and K[[t]]〈〈z〉〉 the formal power series algebra of z over K[[t]]. In [Z6], for each automorphism Ft(z) = z−Ht(z) of K[[t]]〈〈z〉〉 with Ht=0(z) = 0 and o(H(z)) ≥ 1, a NCS (noncommutative symmetric) system ([Z5]) ΩFt has been constructed. Cons...

For given triangular real Lie algebra $\mathfrak{g}$ we construct a certain completion $C^\infty(\mathfrak{g})$ of its universal enveloping algebra. It is Frechet-Arens-Michael algebra, which consists elements polynomial growth and satisfies to the following property: every homomorphism from Banach all whose are has an extension continuous $C^\infty(\mathfrak{g})$. Elements this can be called f...

The non-commutative analytic Toeplitz algebra is the wot– closed algebra generated by the left regular representation of the free semigroup on n generators. We develop a detailed picture of the algebraic structure of this algebra. In particular, we show that there is a canonical homomorphism of the automorphism group onto the group of conformal automorphisms of the complex n-ball. The k-dimensi...

The algebra Sn in the title is obtained from a polynomial algebra Pn in n variables by adding commuting, left (but not two-sided) inverses of the canonical generators of Pn. Ignoring non-Noetherian property, the algebra Sn belongs to a family of algebras like the Weyl algebra An and the polynomial algebra P2n. The group of automorphisms Gn of the algebra Sn is found: Gn = Sn ⋉ T n ⋉ Inn(Sn) ⊇ S...